Mix olive oil, chili powder, paprika, garlic powder, cumin, salt, and pepper in a small bowl. Rub over chicken breasts and let sit for 10 minutes.
Heat a skillet over medium-high heat. Cook chicken 5–6 minutes per side until golden and cooked through (165°F). Squeeze lime juice over the top and set aside.
In a saucepan, combine rice, broth, salsa, cumin, salt, and pepper. Bring to a boil, then simmer covered on low for 15–20 minutes. Let rest 5 minutes, then fluff with a fork.
Melt cheese and half-and-half in a small saucepan over low heat, stirring until smooth. Add chilies and garlic powder. Thin with more milk if needed.
Slice chicken. Plate rice, top with chicken, and drizzle with queso. Add cilantro, tomatoes, jalapeños, or sour cream as desired.