Heat 1 teaspoon extra virgin olive oil in an oven-proof wide pot over medium heat. Add the pork and season with 1 teaspoon kosher salt, ½ teaspoon black pepper, and a pinch of crushed red pepper. Sauté for about 10 minutes until well-browned, breaking it up as it cooks.
Once the pork is completely browned, transfer to a paper towel-lined plate. Drain off all but a thin layer of fat from the pot.
Sauté the aromatics:
Add the onion, carrot, and celery to the pot and sauté for 5 minutes until they begin to soften. Add the garlic and cook for 1 minute until fragrant. Season with ½ teaspoon kosher salt and ½ teaspoon fennel pollen, if using, and toss to coat.
Simmer the ragù:
Pour in the sweet vermouth and bring to a boil. Reduce the heat to medium and simmer for 1 minute. Add the tomatoes and chicken stock and return to a boil.
Reduce the heat to low and add the cooked pork. Taste and add more salt as desired. Reduce the heat to medium-low and partially cover the pot. Simmer for 20 to 30 minutes.
Stir the ragù occasionally and add a few splashes of water as needed to prevent it from sticking. Adjust the heat as needed. You want the liquid to be bubbling, but not aggressively so. The ragù should be thick and meaty, so be careful not to add too much liquid. Taste and add more salt and pepper as needed
Cook the pasta:
Bring a large pot of generously salted water to a boil. Add the rigatoni and cook according to package directions. Reserve 1 cup of the pasta cooking water and drain the pasta.
Make the herbed ricotta:
As the pasta cooks, combine ½ cup ricotta cheese with the minced parsley, 1 tablespoon heavy cream, and 1 tablespoon lemon juice. Whisk until smooth. Taste and season with salt and pepper. Set aside.
Finish the pasta:
Add ½ cup of pasta water to the ragù along with the cooked pasta. Toss to coat and add more pasta water as needed until the pasta is coated. You may need the entire cup or just half depending on your preference. Turn off the heat.
Broil the ricotta cheese:
Turn on the broiler. Spoon dollops of the ricotta cheese over the pasta. Drizzle with a teaspoon of extra virgin olive oil and transfer to the broiler for 2 to 3 minutes until the cheese develops a few brown spots and the edges of the rigatoni crisp up slightly. Watch closely to prevent burning. Remove from the oven.
To serve:
Spoon the pasta into shallow bowls and enjoy with a side salad, garlic bread, or roasted vegetables.