Preheat the oven to 425 degrees F (220 degrees C). Lightly grease a large rimmed baking sheet.
Place chicken on the prepared baking sheet and sprinkle with garlic salt and black pepper. Spread pesto over chicken and top with tomatoes and cheese.
Toss broccoli and oil together in a bowl. Place broccoli around chicken on the baking sheet. Sprinkle salt and pepper on top.
Bake in the preheated oven until broccoli is tender and chicken is no longer pink in the center, 15 to 20 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).