Prepare the lemon vinaigrette: Zest half a teaspoon of lemon peel and squeeze out one tablespoon of lemon juice. Whisk them together with olive oil, feta cheese, and honey in a small bowl, then set aside.
Preheat the oven: Place a 15x10-inch sheet pan inside your oven and preheat to 475°F. Preheating the pan helps achieve perfect caramelization.
Flatten the chicken: Use the flat side of a meat mallet to pound the chicken to ½ inch thickness between two pieces of plastic wrap. This ensures even cooking.
Coat the chicken: Toss the flattened chicken in a bowl with mayonnaise and two cloves of garlic, ensuring it's evenly coated.
Bread the chicken: Mix breadcrumbs, Parmesan cheese, ¼ teaspoon salt, and ¼ teaspoon pepper in a shallow dish. Dip the chicken into the crumb mixture, pressing to adhere. Spray the tops lightly with olive oil cooking spray.
Prepare the vegetables: Combine asparagus, mushrooms, tomatoes, the remaining garlic, olive oil, and the remaining salt and pepper in a large bowl. Toss until well coated.
Assemble and roast: Carefully remove the hot pan from the oven. Place the breaded chicken on one side and the vegetable mixture on the other. Roast everything for 18-20 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender.
Garnish and serve: Drizzle the roasted chicken and vegetables with the lemon vinaigrette and sprinkle fresh dill on top. Serve immediately.