01 - Preheat oven to 400°F. Line a baking dish with foil or parchment paper.
02 - In a small bowl, stir together barbecue sauce, honey, olive oil, smoked paprika, garlic powder, salt, and black pepper until fully combined.
03 - Arrange chicken breasts in the prepared baking dish. Brush each piece generously with the honey barbecue mixture, reserving a small amount for basting.
04 - Bake chicken for 20 to 25 minutes, basting once with reserved sauce midway, until cooked through and the top is caramelized.
05 - While chicken bakes, heat butter and olive oil in a medium saucepan over medium heat. Add chopped onion and diced carrot; sauté for 3 to 4 minutes until vegetables are softened.
06 - Stir in white rice and toast for 1 minute. Add chicken broth, frozen peas, salt, and black pepper. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes or until rice is tender and liquid is absorbed.
07 - Fluff pilaf with a fork. Serve chicken hot over or beside the pilaf. Drizzle any pan juices over the chicken to finish.