Pat the short ribs dry and season them with 3 teaspoons kosher salt and 2 teaspoons black pepper.
Heat 1 tablespoon neutral oil in a wide pot over medium heat. Once hot, add the short ribs in an even layer. Cook for 3 to 5 minutes per side until browned all over. Transfer to a bowl and set aside. Leave any fat and fond in the pot and keep the heat on medium.
Cook the aromatics:
Add the onion, celery, and carrots to the pot and cook for 5 to 7 minutes. Season with salt and pepper to taste.
Brown the tomato paste:
Melt the butter into the aromatics. Add the garlic and cook for 45 seconds. Add the tomato paste and cook, mashing it into the aromatics, for 2 minutes until it begins to deepen in color. Be careful not to burn the garlic.
Pour in the red wine and turn the heat to high. Whisk the wine into the paste and continue until the wine begins to boil. Boil for 3 minutes until it just begins to reduce.
Simmer the ragù:
Add the 2 28-ounce cans of whole peeled tomatoes and bring to a boil. Add the short ribs. Season the sauce with salt, pepper, 1 teaspoon sugar, and crushed red pepper. Add the bay leaves.
Reduce the heat to low. Cover and simmer for 3 hours, until the short ribs are tender, and shred easily with a fork. Check them occasionally to ensure they are not sticking to the pot, and add more liquid as needed.
Allow the ragù to cool and transfer to the refrigerator overnight. See Note 3.
Shred the short ribs:
The next day, remove and discard the hardened fat layer. Remove and discard the bay leaves. Transfer the short ribs to a bowl. Shred the meat using your fingers or two forks, and discard the bones. Set aside.
Finish the ragù:
Turn the heat on the ragù to medium-low and add the shredded short ribs to the sauce. Simmer uncovered for 30 minutes to allow the ragù to thicken. Taste and season with salt, pepper, and crushed red pepper if desired. Turn off the heat and set aside.
Cook the lasagna sheets:
Bring a large pot of generously salted water to a boil. Add as many lasagna sheets as you want and boil them for 8 minutes. Drain and set aside. To prevent the lasagna sheets from sticking, arrange them on parchment paper.
While you wait for the water to boil, prepare the ricotta mixture and the béchamel sauce.
Prepare the ricotta mixture:
Combine all of the ingredients for the ricotta mixture in a bowl. Use a whisk or a hand-mixer and mix until combined. Add ½ teaspoon salt. Taste and add more salt if desired.
Prepare the béchamel sauce:
Warm the milk in a microwave-safe bowl or glass measuring cup for 1 to 3 minutes. Set aside.
Melt the butter in a large saucepan. Once bubbly, add the flour and stir into the butter for 1 to 2 minutes.
Add the milk in 1-cup increments, whisking after each addition. Continue adding the milk until it is incorporated. Cook for 5 to 10 minutes until the béchamel thickens. Season with salt, white pepper, and nutmeg. You should have just over 4 cups of béchamel. Keep warm.
Assemble the lasagna:
Preheat oven to 350ºF.
Grease a 9x13 baking dish. Add 1 cup of the béchamel and use a spoon to smooth it into an even layer.
Place 3 to 4 lasagna sheets over the béchamel.
Spoon 1 cup of the ricotta mixture onto the lasagna sheets and smooth it out with a spoon. Pour 1½ cups of the ragù on top of the ricotta. Finish with 1½ cups of the béchamel sauce.
Place 3 to 4 more lasagna sheets on top. Add the remaining ricotta mixture and 1 ½ cups ragù. Add the remaining 1½ cups of béchamel sauce on top.
Place 3 to 4 more sheets on top. Add 1 cup of ragù and smooth it out. Sprinkle 1 cup mozzarella cheese on top. See Note 4.
Bake the lasagna:
Cover the lasagna with foil. Transfer to the oven for 45 minutes. Remove the foil and bake, uncovered, for 15 minutes. You can also broil the lasagna for 2 to 3 minutes if you like extra browning on the cheese.
To serve:
Allow the lasagna to cool for 20 minutes. Cut into slices and garnish with basil leaves and minced parsley, if you like. Enjoy!
Notes
Note 1: You can use all boneless or all bone-in short ribs. The recipe calls for 3 pounds total using a mix of boneless and bone-in short ribs. If using all bone-in short ribs, use closer to 4 pounds total to account for the bones. Aim for about 2 to 2½ pounds if using all boneless short ribs. You can stick with 3 pounds total regardless of whether you use bone-in or boneless; just keep in mind that all boneless will yield a meatier ragù, and all bone-in short ribs will yield less meat. You can also use a 2- to 3-pound chuck roast cut into large cubes.Note 2: This recipe is for a 3-layer lasagna. A 16-ounce standard box of dry pasta from Barilla has 18 sheets of lasagna. I like to use 9 to 12 sheets of lasagna, meaning I have 3 layers of 3 sheets of lasagna or 3 layers of 4 sheets of lasagna. If you want to use the entire 16-ounce box, I recommend layering 6 sheets across to keep this a 3-layer lasagna, but there will be significant overlap in a 9x13 baking dish. Alternatively, you can make this a 4-layer lasagna by doing the first 3 layers with 5 sheets of lasagna and using just 3 sheets for the top layer. You’ll need to divide the ingredients differently to ensure you have even layers of béchamel, ricotta, ragù, and lasagna sheets.Note 3: Both short ribs and chuck roast are very fatty. If you don’t want to refrigerate them overnight, allow the sauce to cool for up to an hour and use a spoon to skim off the excess fat. Then, remove and shred the meat with your hands or two forks. I recommend refrigerating the sauce overnight to make removing the fat layer simple.Note 4: You can assemble lasagna and refrigerate it 36–48 hours in advance. If you'd like to assemble it more than two days in advance, cover it with two layers of tightly wrapped foil and transfer it to the freezer. If the lasagna is frozen (not thawed), bake it in the oven for up to 90 minutes. If you've completely thawed the lasagna from the freezer, it will need up to 60 minutes to bake.