Heat a large skillet over moderate heat. Add oil, butter, garlic and shallots. Gently sauté shallots for 3 to 5 minutes to develop their sweetness.
Add vodka to the pan (3 turns around the pan in a steady stream will equal about 1 cup). Reduce vodka by half, this will take 2 or 3 minutes. Add chicken stock, tomatoes.
Bring sauce to a bubble and reduce heat to simmer. Season with salt and pepper.
While sauce simmers, cook pasta in salted boiling water until cooked to al dente (with a bite to it). While pasta cooks, prepare your salad or other side dishes.
Stir cream into sauce. When sauce returns to a bubble, remove it from heat. Drain pasta. Toss hot pasta with sauce and basil leaves. Serve pasta with crusty bread.