Boil pasta in a large pot of well-salted boiling water according to package directions. Reserve ½ cup of the pasta cooking water. Drain.
While the pasta cooks, heat the olive oil and butter over medium heat in a large skillet until the butter melts. Add the shallot, season with salt and pepper, and cook until lightly golden brown, 2 to 3 minutes. Stir in the garlic, red pepper flakes, and tomato paste. Cook, stirring constantly, for 1 minute.
Add the cream, whisking to combine, and cook for 4-5 minutes. Turn off the heat, and whisk in the vodka. Turn back on the heat, and whisk the sauce for about 4-5 more minutes to allow the alcohol to cook off.
Stir in ¼ cup of the reserved pasta water, whisking until thick. Continue cooking, whisking occasionally, until the sauce reaches the desired consistency, about 5-10 minutes. Add additional pasta water, as necessary (the starches in the pasta water help to thicken the sauce as it simmers). Taste and season with salt and pepper to taste.
Add the basil and cooked pasta to the sauce; stir to coat.
Garnish with grated Parmesan cheese and chopped fresh herbs, if desired.