Heat a large skillet over medium heat and melt 2 tablespoons of the butter.
Add the diced onion, red bell pepper, and green bell pepper; cook, stirring occasionally, until softened, about 2–3 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Push the vegetables to one side of the skillet and add the remaining 1 tablespoon butter to the empty side; add the rice and toast, stirring, for 1–2 minutes.
Stir in the chicken broth, sour cream, shredded rotisserie chicken, diced green chiles, lime juice, salt, ground cumin, and chili powder; bring to a boil.
Once boiling, reduce heat to low, cover, and simmer for 15–20 minutes, or until the rice is tender and has absorbed most of the liquid; add a splash more broth if needed to finish cooking.
Sprinkle the shredded cheddar over the cooked rice, cover, and let sit until the cheese melts, about 1–2 minutes.
Garnish with cilantro and serve with sour cream, guacamole, and diced tomatoes as desired.
