1. In a pan over medium heat, sauté the shallots, garlic, and basil sprig in olive oil for a couple of minutes, until the shallots are translucent.
2. Add the tomato paste and cook for another 2–3 minutes, stirring often, until it turns a deep red color.
3. Deglaze the pan with vodka. Once the alcohol cooks off and the flames die down, stir in the Calabrian chili paste and cherry tomatoes.
4. Let the mixture simmer, using a wooden spoon to gently crush the tomatoes as they soften.
5. Once all the tomatoes have burst, pour in the heavy cream. Simmer on low heat for 5 minutes, then remove the basil stem.
6. Blend the sauce until smooth, then strain it to remove any skins or seeds.
7. Season with salt and pepper to taste, and keep warm while you cook the pasta in salted boiling water until al dente (a couple minutes less than the package instructions).
8. Add the pasta to the sauce over medium-low heat along with the butter and a generous grating of Parmesan cheese.
9. Toss until the sauce coats the pasta, adding pasta water as needed to loosen it.
10. Once the sauce clings beautifully to the pasta, serve immediately with more grated Parmesan on top.
