Fill a large pot with water, add a generous pinch of salt, and bring to a rolling boil.

Add pasta to boiling water and cook until just shy of tender, about 2 minutes less than package directions specify.

While the pasta cooks, mince garlic finely or use a microplane to create a paste-like consistency.

Heat olive oil in a large saucepan over medium-high heat, then add minced garlic and red pepper flakes; stir constantly for about 30 seconds until fragrant.

Add tomato paste to the garlic and oil, stirring constantly for 2 minutes to bloom and deepen the umami flavor.

Pour vodka into the pan, stirring to scrape up any browned bits, and let it simmer for 2 minutes to cook off the raw alcohol taste.

Add crushed tomatoes, salt, black pepper, and sugar; stir well to combine.

Reduce heat to medium and simmer the sauce for 8 to 10 minutes, stirring occasionally until slightly thickened.

Drain the pasta, reserving 1 cup of the starchy cooking water.

Reduce heat to medium-low, then slowly pour in heavy cream while stirring constantly to prevent curdling; add butter and stir until melted and glossy.

Add the drained pasta directly to the sauce, stirring gently to coat; add a splash of reserved pasta water and stir until the sauce clings evenly to the pasta.

Remove from heat, stir in fresh basil, and adjust seasoning with additional salt or pepper as needed.