Pat the chicken thighs dry with paper towels. Sprinkle the garlic powder, salt, and cumin evenly over both sides of the chicken.
Heat a large skillet over medium-high heat. Add the vegetable oil and swirl to coat the pan.
Add the chicken thighs to the hot skillet in a single layer. Cook without moving 3–4 minutes, then flip and cook 2–3 minutes more, until browned on both sides but not fully cooked through. Remove the chicken from the skillet and set aside.
Pour the 2 cups chicken broth into the hot skillet. Use a spatula or wooden spoon to scrape and loosen any browned bits from the bottom of the pan.
Add the 1 cup salsa verde, the drained can of sweet corn, and the 1 cup long-grain rice to the skillet. Stir once to combine and distribute the rice.
Increase heat to bring the mixture to a gentle boil. Immediately cover the skillet, reduce heat to low so the contents simmer gently, and cook undisturbed for 15 minutes.
After 15 minutes, remove the lid, stir the rice, and nestle the seared chicken thighs back into the rice so they sit partly submerged in the liquid. Replace the lid and continue to cook on low for 10–15 minutes more, or until the rice is tender, the liquid is absorbed, and the chicken reaches an internal temperature of 165°F.
Sprinkle the 1/2 cup Colby Jack cheese evenly over the top of the rice and chicken. Cover the skillet and let sit 1–2 minutes, or until the cheese has melted.
Remove the skillet from the heat and serve warm.