Preheat oven to 350 degrees.
Cut each piece of chicken in half. Pound chicken to a uniform thickness of 3/8 inch; set aside.
Mix dried mushroom pieces and 1 tablespoon flour in a shallow dish. In another shallow dish, beat eggs to a slight froth.
Season with salt and pepper the chicken pices. Lightly coat each piece of chicken with egg, then dip into mushroom mixture, patting mushrooms into place, coating lightly. Stack chicken on a plate, separating the pieces with waxed paper.
Reserve the remaining dried mushroom mixture to use in the sauce.
Heat oil in an 8- or 10-inch nonstick skillet over high heat. When a pinch of flour sizzles in the oil, add chicken, in batches if necessary; cook for 2 minutes on each side. Arrange chicken in an 11-by-14-inch baking dish. Place dish in oven; bake for 12 minutes or until done.
Meanwhile, return skillet to the stove. Add butter and melt over medium-high heat. Stir in remaining mushroom mix, remaining 2 1/2 tablespoons flour and garlic. Cook, stirring constantly, until golden brown. Reduce heat to medium; slowly stir in broth. Stir in lemon zest and juice; cook, stirring, until thickened, about 2 minutes. Remove from heat; stir in capers. Set aside and keep warm.
When chicken is done, arrange on serving plates; top with sauce.