Preheat the oven to 375°F. Grease a 9x13 inch baking dish. Set aside.
Cook the pasta 2-3 minutes less than the package directions. Reserve 1 cup of the pasta water and set aside. Drain the pasta and rinse it under cold water. Set aside.
Heat a pan over medium high heat. Add in the spicy Italian sausage. Cook and crumble until browned and cooked through. Remove the sausage from the pan.
Pour the olive oil into the same pan. Add in the red onion and garlic. Sauté for 2-3 minutes until the onion turns translucent. Stir in the tomato paste until well combined and cook for 1 minute. Then pour in the vodka. Cook and mix until the vodka is absorbed and evaporates from the pan.
Add in the heavy cream, red pepper flakes, kosher salt, and ground black pepper. Mix until combined. Add the cooked sausage, pasta, and basil back into the pan and mix. Then add in the reserved pasta water and unsalted butter. Cook until the butter has melted and the sauce comes to a simmer. Add in 1/2 a cup of the mozzarella cheese and a 1/2 cup of the parmesan cheese. Mix until the cheeses are incorporated.
Pour half of the pasta into the prepared baking dish. Dollop half of the burrata and pesto, in small spoonfuls, on top of the pasta. Spread the remaining half of the pasta on top. Dollop the remaining burrata and pesto over top. Sprinkle the remaining mozzarella and parmesan over the pasta.
Bake the pasta in the oven for 20-25 minutes until the cheese has melted. Change the oven setting to broil and cook for 2-4 minutes until the cheese has started to slightly brown and bubble. Remove the pasta from the oven. Garnish with additional chopped basil and enjoy!