Preheat the oven to 375 degrees F (190 degrees C). Coat a 9x13-inch casserole dish with cooking spray.

Melt butter in a medium skillet over medium heat. Add flour and garlic; stir constantly until garlic is fragrant and flour and butter are well combined, about 1 minute. Stir in chicken broth and half-and-half. Bring to a boil, stirring frequently, until sauce is bubbly and thick, about 5 minutes.

Remove from heat; stir in ½ cup Parmesan cheese, lemon juice, capers, salt, and black pepper; set aside.

Slice each chicken breast lengthwise into 2 cutlets; place in a single layer in the prepared dish. Season with salt and black pepper. Spread sauce evenly over cutlets; top with lemon slices.

Combine remaining ¼ cup Parmesan cheese and bread crumbs in a small bowl; sprinkle evenly over casserole.

Bake in the preheated oven until an instant-read thermometer inserted into the cutlets reads 165 degrees F (74 degrees C), 20 to 25 minutes. Garnish with parsley; serve warm.