Preheat oven to 400ºF.

Heat neutral oil in a wide pot over medium-high heat. Add half the mushrooms and cook for 8–10 minutes until they turn golden brown and crisp up around the edges. Season with salt and pepper and transfer to a bowl. Add more oil and the remaining mushrooms and cook an additional 8–10 minutes. Transfer to the bowl of mushrooms.

Add the onion to the pot and cook for 5–6 minutes until it softens. Return the mushrooms to the pot and add the garlic, dry thyme, and a big pinch of crushed red pepper.

Turn the heat to high, and as soon as the mushrooms begin sizzling hard in the pot, pour in the sweet vermouth. Stir to lift anything stuck to the bottom of the pot and bring it to a boil. Reduce heat and cook for 3–4 minutes.

Add the crushed tomatoes and tomato sauce to the pot and boil. Add a pinch of sugar if you like. Reduce heat and stir in the basil and parsley. Simmer, uncovered, for 30–40 minutes. Taste and season with salt and pepper.

Bring a large pot of salted water to a boil. Add the pasta and cook until al dente. Drain and transfer to a large bowl. Add 3/4 of the sauce from the pot and toss to coat. Set aside.

Melt the butter in a pot over medium heat. Once bubbly and melted, add the flour. Stir it into the butter and cook for 1–2 minutes until nutty and fragrant.

Add a ladle of the milk and constantly whisk until a slurry forms. Continue ladling in the milk, whisking after each addition, until all the milk has been incorporated and the sauce is smooth. Simmer over medium-low for 5–10 minutes or until the béchamel is thick. Season with white pepper and salt. Turn off the heat.

Pour the remaining half of the pasta on top and cover with the remaining sauce. Use the back of your spoon to smooth everything into an even layer. Finish with the remaining béchamel and smooth it out. Sprinkle the remaining mozzarella and Parmigiano-Reggiano on top. Finish with freshly cracked black pepper.

Transfer to the oven and bake for 30 minutes until bubbly. At the end of cooking, turn on the broiler and broil the top for 1–2 minutes until golden brown. Remove from the oven and let stand for 5–10 minutes.

Sprinkle fresh basil on top of the pasta and serve. Enjoy!