Preheat the oven to 425 degrees F (220 degrees C). Lightly grease a large sheet pan.
Season chicken with garlic salt and pepper; place onto the prepared sheet pan. Spread pesto over chicken, then top with tomatoes and mozzarella.
Toss broccoli and oil together in a bowl; season with salt and pepper. Scatter around chicken on the baking sheet.
Bake in the preheated oven until broccoli is tender and chicken is no longer pink in the center and the juices run clear, 15 to 20 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).