Preheat the oven to 350 degrees F (175 degrees C).

Melt butter in a large skillet over medium-high heat. Cook chicken until lightly browned on both sides, 5 to 7 minutes. Place in a baking dish.

Stir lemon juice and zest into the leftover butter in the pan, and cook over medium-low heat, stirring, for 3 to 4 minutes. Stir in half-and-half slowly. Stir in 1/4 cup Parmesan cheese until sauce is smooth. Pour sauce over chicken.

Bake in the preheated oven until chicken is no longer pink in the center and juices run clear, 20 to 30 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Sprinkle remaining 1/4 cup Parmesan cheese on top.