Cook penne pasta in a large pot of salted boiling water until al dente. In a large pot with deep sides, heat olive oil and butter over medium heat. Add diced shallot, then cook until translucent. Add chopped garlic and red pepper flakes, then stir and cook. Stir in tomato paste.
Reduce the heat to medium-low, then add vodka. Cook until reduced by half. Stir in heavy cream and grated Parmesan, then simmer until thickened.
Add cooked pasta to the pan with the vodka sauce along with the reserved water. Cook, stirring often Finally, remove the pan from the heat, then stir in remaining butter and loosely packed basil leaves.