Cook pasta in a large pot of salted water according to package directions until al dente. Reserve ¼ cup pasta cooking water before draining.
Melt butter in a large deep sauté pan over medium-low heat.
Add diced onions, season with salt and pepper, and cook until softened, about 5 to 7 minutes.
Add garlic and cook until fragrant, about 1 minute, stirring frequently.
Stir in tomato paste and cook, stirring occasionally, until it darkens in color, about 5 minutes.
Pour in vodka and cook until mostly evaporated, about 1 minute.
Add heavy cream and red pepper flakes, cook while stirring occasionally for 2 minutes until slightly thickened.
Add drained pasta and reserved pasta water to the sauce, tossing to coat the pasta thoroughly.
Turn off heat, stir in parmesan cheese until melted and combined.
Serve topped with additional parmesan and fresh basil leaves.