Heat oil in large skillet over medium. Add shallot and garlic and cook, stirring occasionally, until softened - about 5 minutes
Add tomato paste and cook, stirring occasionally, until paste is brick red and starts to caramelize, about 5 minutes
Add vodka and cook, stirring constantly, until liquid is mostly evaporated, about 2 minutes
Add cream and red pepper flakes and stir until well blended
Season to taste with salt and pepper and remove from heat
Meanwhile, cook 1 lb pasta according to package directions. Reserve 1 cup pasta liquid and drain. Add pasta to skillet with sauce along with butter and 1/2 cup pasta cooking liquid
Cook over medium-low heat, stirring constantly and adding more pasta water as needed until butter has melted and a thick, glossy sauce has formed, about 2 minutes
Season with salt and pepper o taste, and add 1oz Parmesan, tossing to coat
Top with basil and more Parmesan to serve