Season chicken breasts on both sides with the salt, garlic powder, and black pepper. Drizzle 1 tablespoon olive oil into a medium skillet set over medium heat. Arrange chicken breasts in the skillet. Brown the chicken on both sides, about 3 minutes per side.
Place the skillet into the preheated oven and bake until juices run clear when pricked with a knife and the internal temperature registers 165º F when checked with an internal thermometer, about 20 minutes.
Arrange the cheese on top of the chicken breasts and top with the cherry tomato halves and return to the oven until the cheese melts, about 3 minutes.
Remove from the oven and top with basil glaze and basil leaves for serving. Salt and pepper to taste.