Heat 2 teaspoons butter in a large skillet over medium heat until melted.
Add 1/2 cup chopped onion and 2 minced garlic cloves; cook, stirring, until the onion is tender and fragrant, about 3–4 minutes.
Stir in 1 1/3 cups chicken broth, 1 cup salsa, and 1/4 teaspoon garlic powder; bring the mixture to a boil.
Add 1 cup uncooked long-grain rice, stir, and return to a boil.
Place 1 pound boneless skinless chicken breasts on top of the rice; reduce heat to low, cover, and simmer for 20–25 minutes, turning the chicken once halfway through, until the rice is tender and chicken reaches 165°F (74°C).
Remove skillet from heat; sprinkle 1/2 cup shredded Mexican cheese over the chicken and rice, cover, and let stand until the cheese melts.
Garnish with chopped fresh cilantro if desired, then serve.