Bring a large pot of salted water to a boil.

Heat 2 Tbsp. oil in a large Dutch oven or pot.

Cook onion and garlic, stirring constantly, just until onion is starting to brown around the edges, 5–7 minutes.

Add tomato paste and red pepper flakes and stir to coat the onion. Cook, stirring often, until paste is deep red and starting to brown and stick to the bottom of pot, 5–7 minutes.

Add vodka, scraping up brown bits; reduce heat to low.

Scoop ¼ cup boiling water from the pot and add heavy cream. Gradually pour the cream mixture into the onion mixture and cook, stirring, until a smooth sauce forms. Remove from heat.

Cook pasta until al dente.

Scoop out 1 cup of pasta cooking liquid.

Return the pot to low heat. Using a slotted spoon, transfer the pasta to the pot.

Stir in ½ cup pasta cooking liquid and half of the Parmesan, stirring constantly to melt.

Pasta should be coated with a smooth, glossy sauce. Season with salt; add more pasta cooking liquid if sauce is too thick.

Divide pasta among bowls. Top with basil and remaining Parmesan and drizzle with a little oil.