• 3 tbsp. unsalted butter, cut into 3 pieces
• 1 tbsp. chopped fresh parsley
Working with 1 chicken breast at a time, starting on thick side, cut breasts in half horizontally. Using meat pounder, gently pound each cutlet into even 1/2-inch thickness between 2 pieces of plastic wrap. Pat cutlets dry with paper towels and season with 1/2 teaspoon salt and pepper; set aside.
Heat 2 tablespoons oil in 12-inch nonstick skillet over medium-high heat until just smoking. Add mushrooms, bell pepper, shallot and remaining 1/4 teaspoon salt, and cook until liquid has evaporated and vegetables begin to brown, 8 to 10 minutes. Add capers and garlic and cook until fragrant, about 1 minute. Add broth and wine and bring to boil, scraping up any browned bits. Cook until slightly thickened and mixture is reduced to 2 cups (measured with vegetables), about 8 minutes. Set aside in measuring cup. Wipe out skillet with paper towels.
Spread flour in shallow dish. Working with 1 cutlet at a time, dredge cutlets in flour, shaking off excess and transfer to plate. Heat 2 tablespoons oil in now-empty skillet over medium-high heat until just smoking. Add 4 cutlets and cook until golden and cooked through, about 2 minutes per side. Transfer to platter and tent loosely with aluminum foil. Repeat with remaining 4 cutlets and remaining 2 tablespoons oil.