Preheat the oven to 400°F and line a baking sheet with parchment paper.
Pound the chicken breasts to even thickness, then season both sides with salt and pepper.
Beat the egg in a shallow bowl. In another bowl, mix the breadcrumbs with ¼ cup of the Parmesan.
Dip each chicken breast in the egg, then coat it in the breadcrumb mixture and place it on the prepared baking sheet.
Bake the chicken for 20 minutes. Remove the sheet from the oven and spoon marinara sauce over each piece.
Sprinkle the mozzarella and remaining Parmesan over the sauce. Return the sheet to the oven and bake 10 more minutes until the cheese melts and bubbles.
While the chicken finishes baking, place the mixed greens, cherry tomatoes, and cucumber in a large bowl.
Drizzle the salad with olive oil and balsamic vinegar, then toss gently to coat.
Serve each chicken piece with a portion of the side salad on the plate.