1. Preheat oven to 400°. Lightly coat a 15x10x1-in. baking pan with cooking spray.
2. In a shallow bowl, whisk egg. In a separate shallow bowl, stir together the next 5 ingredients. Dip chicken breast in egg; allow excess to drip off. Dip in crumb mixture, patting to help coating adhere. Repeat with remaining chicken. Place chicken breasts in center third of baking pan. Spritz with cooking spray.
3. Bake 10 minutes. Remove from oven. Spread broccoli in a single layer along both sides of sheet pan (if broccoli is frozen, break pieces apart). Return to oven; bake 10 minutes longer. Remove from oven.
4. Preheat broiler. Spread marinara sauce over chicken; top with shredded cheese. Broil chicken and broccoli 3-4 in. from heat until cheese is golden brown and vegetables are tender, 3-5 minutes. If desired, sprinkle with basil
