Cook pasta in a large pot of salted boiling water until al dente, according to package instructions. Reserve ½ cup of the cooking water; drain.
Meanwhile, heat olive oil and butter in a large skillet or Dutch oven over medium heat until the butter melts. Add the garlic and onion; cook until the onion softens, about 3 minutes. Add the oregano and tomato paste, cook, stirring constantly for 1 minute. Turn off the burner and pour in the vodka. Turn the heat to medium-high, bring the liquid to a bubble, cook for 1-2 minutes.
Reduce the heat to medium-low; stir in tomato sauce, pesto, red pepper flakes, salt and pepper. Simmer for 2-3 minutes. Gradually stream in the cream, stirring constantly.
Reduce the heat to low and simmer for 1-2 more minutes, until heated through. Taste and season with additional salt, pepper or red pepper flakes, if necessary. Add the cooked pasta to the skillet and toss to combine. Stir in a little bit of the reserved cooking water, if necessary, to thin the sauce to the desired consistency. Garnish with freshly-grated Parmesan and fresh basil.