Preheat oven to 350 degrees F (175 degrees C). Line a 9x13-inch baking pan with non-stick aluminum foil.
Place chicken pieces in the pan. Sprinkle 1 tablespoon of rosemary, cayenne, salt, and pepper over chicken. Add yellow squash, zucchini, onion, and grape tomatoes; mix and spread evenly. Drizzle with olive oil. Sprinkle remaining 2 tablespoons of rosemary, minced garlic, garlic salt, and parsley on top. Cover with aluminum foil.
Bake in the preheated oven, stirring halfway through, until chicken is tender, about 45 minutes.
Increase oven temperature to 375 degrees F (190 degrees C). Uncover baking pan; baste chicken with accumulated juices. Bake, uncovered, until browned and an instant-read thermometer inserted into the center reads at least 165 degrees F (74 degrees C), about 15 minutes more.