In a sauté pan, heat the oil and butter. Add the onion and carrot and cook gently until soft but not brown, 2-3 minutes. Add the garlic and anchovy and cook, stirring, 1 minute. Add the fennel slices, parsley, bay leaf and vermouth and simmer until fennel is soft, 8-10 minutes.
Sprinkle the tuna on both sides with salt and pepper. Lay it on top of the vegetable