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Step 1
Preheat oven to 375 degrees F. Coat a large rimmed baking sheet with cooking spray.
Step 2
Make crosswise cuts every 1/2 inch along both chicken breasts, slicing almost to the bottom but not all the way through. Sprinkle chicken with 1/4 teaspoon each salt and pepper. Fill the cuts alternately with tomato and mozzarella slices. Brush with pesto. Transfer the chicken to one side of the prepared baking sheet.
Step 3
Toss broccoli, oil and the remaining 1/4 teaspoon each salt and pepper in a large bowl. If there are any tomato slices left, mix them in. Transfer the broccoli mixture to the empty side of the baking sheet.
Step 4
Bake until the chicken is no longer pink in the center and the broccoli is tender, about 25 minutes. Cut each breast in half and serve with the broccoli.