Stir water, kosher salt, and sugar together until the salt and sugar dissolve completely into a brine.

Put chicken breasts in a large resealable plastic bag; pour brine into the bag with the chicken. Squeeze air from the bag and seal. Refrigerate for 1 hour.

Preheat oven to 350 degrees F (175 degrees C). Grease a 13x9x2-inch baking dish.

Mix Parmesan cheese, bread crumbs, parsley, salt, and black pepper together in a bowl; spread about 1/3 of the mixture into the bottom of the prepared baking dish.

Remove chicken from the brine, shake off excess liquid, and pat dry. Discard remaining brine.

Coat chicken with olive oil. Arrange chicken atop the Parmesan cheese layer in the baking dish. Sprinkle remaining Parmesan cheese mixture over the chicken.

Mix garlic, margarine, and lemon juice together in a small bowl; drizzle over chicken.

Cook chicken breasts until no longer pink in the center and the juices run clear, 25-30 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).

Switch oven to broil. Sprinkle cheese over the chicken breasts.

Heat oven's broiler. Cook chicken under the broiler until the cheese is melted and golden brown, about 5 minutes more.