Preheat the oven to 350 degrees F (175 degrees C).

Heat vegetable oil in a large skillet over medium heat. Season one side of chicken breasts with 1/2 of the cumin, 1/2 of the garlic powder, salt, and black pepper; arrange chicken breasts seasoned-side down in hot oil. Fry until chicken is lightly browned on the bottom, 4 to 5 minutes.

Season the top of each chicken breast with remaining cumin, remaining garlic powder, salt, and black pepper; flip chicken and cook until other side is lightly browned, 4 to 5 minutes. If the skillet gets dry, pour in just enough salsa juice to keep it from burning.

Transfer chicken breasts to a 9-inch square baking dish; sprinkle with Mexican cheese blend. Loosen drippings from the skillet with a little more salsa juice and pour on top of chicken breasts. Spoon salsa over cheese layer.

Bake chicken breasts until no longer pink in the center and the juices run clear, 20 to 25 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).