Heat a large skillet over moderate heat. Add oil, butter, garlic, and shallots. Gently saute shallots for 3 to 5 minutes to develop their sweetness.
Add vodka to the pan, reduce vodka by half, this will take 2 or 3 minutes.
Add chicken stock and 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.
Stir cream into sauce. When sauce returns to a bubble, remove it from heat.
Drain pasta. Toss hot pasta with sauce and basil leaves.
