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["Position a rack in the center of the oven and heat the oven to 425F.", "Make a lengthwise horizontal slice almost through each chicken breast and open each up like a book.", "Flatten the chicken with a meat mallet until it is 1/4"" thick.", "put the cheese, breadcrumbs, 3 Tbsp capers, lemon zest, and 1 Tbsp parsley in a mini chopper of food processor and pulse a few times to combine.", "Sprinkle the mixture on top of the chicken breasts.", "Fold each breast closed and secure with toothpicks.", "Sprinkle the breasts with salt and pepper.", "Heat 1 Tbsp butter and the oil in a large (12""), heavy-duty, oven-proof skillet over medium-high heat until the butter melts and starts to foam, about 2 minutes.", "Add the chicken and cook, without touching, until it browns and easily releases from the pan, about 2 minutes.", "Turn the chicken and cook the other side until browned, about 2 more minutes.", "Add the garlic and the remaining 1 Tbsp capers to the skillet, transfer the pan to the oven, and roast uncovered until the chicken cooks through (165F), about 8 minutes.", "Transfer the chicken to a serving platter and tent with foil.", "Set the skillet over medium-high heat; add the chicken broth and cook, scraping the bottom of the pan with a wooden spoon to loosen any brown bits, until it reduces by half, about 2 minutes.", "Remove from heat and whisk in 2 Tbsp of the lemon juice and the remaining 2 Tbsp of butter.", "Taste and add more lemon juice, salt, and pepper, if needed.", "Serve the chicken drizzled with the butter sauce and sprinkled with the remaining 1 Tbsp parsley."]