Preheat an oven to 375 degrees F (190 degrees C). Grease an 8x8-inch baking dish.
Place each chicken breast between two sheets of heavy plastic (resealable freezer bags work well) on a solid, level surface. Firmly pound the chicken with the smooth side of a meat mallet to an even thickness of about 1/4 inch. Sprinkle each side with salt and pepper.
Place 4 spears of asparagus down the center of a chicken breast, and spread about 1/4 cup of mozzarella cheese over the asparagus. Repeat with the other chicken breast, and roll the chicken around the asparagus and cheese to make a tidy, compact roll. Place the rolls seam sides down in the prepared baking dish, and sprinkle each with about 2 tablespoons of bread crumbs.
Bake in the preheated oven until the juices run clear when pricked with a fork, about 25 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).