Bring a large pot of salted water to a boil. Add 8 ounces of penne pasta and cook according to package instructions until al dente, usually about 10-12 minutes. Reserve 1/2 cup of pasta water, then drain the pasta and set aside.
While the pasta cooks, heat 2 tablespoons of olive oil over medium heat in a large skillet. Add the finely chopped shallot and sauté for 2-3 minutes until softened and fragrant. Stir in the minced garlic and cook for an additional 30 seconds, being careful not to let it burn.
Stir in 1 teaspoon of Calabrian chili paste and cook for 1 minute to release its smoky heat. Pour in the 14-ounce can of crushed tomatoes, stirring to combine. Simmer the sauce for 8-10 minutes, allowing it to thicken slightly.
Reduce the heat to low and carefully add 1/2 cup of heavy cream, stirring to blend the sauce until smooth and creamy. Season with 1/2 teaspoon salt and 1/4 teaspoon black pepper. If you like an extra kick, sprinkle in 1/2 teaspoon of red pepper flakes.
Add the drained penne pasta to the skillet with the sauce. Toss to coat the pasta evenly, adding reserved pasta water a splash at a time if the sauce feels too thick. Stir in 1/2 cup of freshly grated Parmesan cheese until melted and combined.
Remove from heat and stir in 1 tablespoon of chopped fresh basil. Serve immediately with extra Parmesan on the side for topping. This Spicy Calabrian Chili Vodka Penne is best enjoyed hot and fresh!