Heat a large saucepan over medium-high heat. Add the olive oil and the onions and cook until onions are softened and translucent, about 5 minutes. Add the garlic and cook for another 30 seconds. Add the tomato paste and cook until caramelized about 5 minutes.
Deglaze with vodka. Cook until the liquid is almost completely evaporated. Add the canned tomato and the Calabrian chili, reduce the heat to medium, and simmer for about 15 minutes, stirring occasionally. While the sauce simmers, cook the pasta al dente in boiling salted water according to package directions.
Once the sauce has reduced, stir in the heavy cream. Turn off the heat until you're ready to add the pasta.
Transfer cooked pasta directly into the sauce, save the pasta water, and turn the heat to medium. Add about 1/4 cup of pasta water and simmer the pasta in the sauce for about 3 minutes. This will allow the pasta to absorb the sauce. Add more pasta water as needed.
Turn off the heat and add the parm, butter, and another splash of pasta water. Mix to combine until you have a glossy emulsified sauce.
