Heat 2 tablespoons butter in a saucepan over medium heat; cook and stir chicken, 1 packet sazon seasoning, and 1 teaspoon garlic salt, shredding chicken as it cooks until no longer pink in the center and juices run clear.

Bring rice and water to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender, and the liquid has been absorbed.

Stir black beans, 1 packet sazon seasoning, and 1 teaspoon garlic salt together in a microwave-safe bowl. Cook in microwave until heated through.

Place each tortilla on a work surface; layer half of each tortilla with bean-rice mixture, Mexican cheese, shredded chicken, and more Mexican cheese. Fold each tortilla in half. Spread a thin layer of softened butter atop each quesadilla.