Bring a large pot of salted water to a boil. Cook off the rigatoni according to package directions. Drain.
Heat 1 tablespoon olive oil in a large oven-safe skillet over medium. Saute the onion and shallot until softened, about 4-5 minutes. Stir in the garlic, thyme, paprika, red pepper flakes, and tomato paste. Pour in the vodka and bring to a simmer until reduced by half, about 2-3 minutes.
Add the crushed tomatoes, pesto, butter, and coconut milk or heavy cream. Simmer until slightly thickened, about 5-8 minutes. Stir in 1 cup of parmesan and the spinach until the cheese melts and the spinach wilts, about 2-3 minutes longer.
Dump the pasta into the sauce and toss to coat. If needed, transfer the pasta and sauce to an oven-safe casserole dish. Top with the fontina, mozzarella, gouda, and remaining 1/4 cup of parmesan. Bake for 12-15 minutes until the cheese melts, bubbles, and turns golden in spots. Serve hot with fresh herbs, as desired.