Fill a large pot of water, with 2 tsp of salt, and bring to a boil. Cook the pasta according to the package directions (until al dente). Drain.
Chop the garlic and grate the Parmesan. Set aside.
Heat a large pan over medium-high heat. Add the oil and heat until it shimmers. Add the chopped garlic and red pepper. Cook, stirring, until fragrant but not browned, about 30 seconds.
Slowly pour in the vodka and cook until it is nearly evaporated, being careful to keep the vodka bottle away from the flame.
Add the canned tomatoes and bring to a simmer, breaking up the tomatoes with a spatuala. Lower heat to medium and continue to simmer for 10 minutes. Add the cream and grated Parmesan and simmer 3-5 minutes longer. Season with extra salt to taste.
Add the cooked and drained pasta and stir to coat with the sauce.
Remove from heat. Stir in the basil and top with extra Parmesan.