Heat a pot of water to a boil, salt the water and cook pasta to al dente.
Heat a deep large skillet with 1 tablespoon extra-virgin olive oil over medium-high heat. Add bacon and crisp 3 to 4 minutes. Add onions, garlic, bay leaf and mushrooms, season with salt and pepper and cook until tender but not browned, 5 minutes. Add tomatoes, crush them up with a wooden spoon and simmer 15 minutes on low heat.
Season the fish with salt and pepper. Dust fish with flour and shake off excess.
Heat 2 tablespoons extra-virgin olive oil in a large skillet over medium high heat. Cook fish 4 minutes on each side.
While fish cooks, stir peas into sauce, return to bubble and stir in mascarpone cheese. Adjust seasoning.
Remove fish from skillet to a platter and cover loosely with foil to keep warm. Reduce heat to medium and add butter to pan. Brown butter, 2 to 3 minutes, stir in balsamic and simmer 1 to 2 minutes to reduce by half. Pour the brown butter and vinegar over fish.
Drain pasta, toss with sauce and wilt basil into pasta.
Serve fish with pasta alongside.