Place duck breasts between a zipper-lock bag and pound lightly until each piece is approximately 1/8-inch thick. Season with salt and pepper. Place flour in a shallow dish and dredge seasoned duck lightly in flour.
Heat half of the butter with the olive oil in a large skillet over medium-high heat. Add duck, a few pieces at a time, browning evenly on both sides – about 1 minute per side. When cooked, transfer to a plate with paper towels to drain. Cover with foil and keep warm.
When all duck is browned, add lemon juice, garlic, wine and broth to pan. Stir to scrape bits and add mushroom, capers and Italian seasoning. Cook until liquid is reduced to 1/3 cup. Stir in remaining butter until melted. Stir in tomato.
Mound pasta on plates, arrange cooked duck over pasta and spoon sauce over. Top with Parmesan cheese.