In a large bowl, combine olive oil, garlic, honey, lime juice, chili powder, salt, and black pepper. Add the chicken thighs and toss until evenly coated. Let marinate for 10–15 minutes while preparing the remaining ingredients.
Heat a large deep skillet or saute pan over medium-high heat. Add the chicken thighs in a single layer. Cook for 2–3 minutes per side until lightly browned. The chicken does not need to be fully cooked. Transfer the chicken to a plate and set aside.
Reduce heat to medium. Add the rinsed rice, chicken broth, and frozen mixed vegetables to the pan. Stir everything together and bring to a gentle simmer.
Place the browned chicken thighs on top of the rice mixture. Cover with a lid. Reduce heat to low and cook for 18–20 minutes, or until the rice is tender and the chicken reaches an internal temperature of 165°F. Remove from heat and let rest, covered, for 5 minutes.
While the pan rests, combine mayonnaise, sour cream, lime juice, honey, garlic powder, and salt in a small bowl. Mix until smooth.
Fluff the rice gently with a fork. Sprinkle with cilantro if using. Drizzle with the creamy lime sauce and serve with extra lime wedges if desired.