Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving 1 cup of the pasta cooking water.
While the pasta is working, in a large skillet, heat the EVOO, 2 turns of the pan, over medium heat. Add the butter and cook until foaming. Stir in the fennel, onion and garlic; season with salt and pepper. Partially cover and cook, stirring occasionally, for 10 minutes. Stir in the tomatoes with their liquid and the vodka. Break up the tomatoes with a potato masher. Cook the sauce for 10 minutes. Stir in the cream, tarragon and basil; simmer briefly. Season with salt and pepper.
Stir the reserved pasta cooking water into the sauce. Add the pasta and toss to combine. Serve the pasta in shallow bowls and pass the cheese at the table.
