Rinse the rice under cold water until the water runs clear. In a medium saucepan, combine the rice and 2 cups of water. Bring to a boil over medium-high heat, then reduce heat to low, cover, and simmer for 15 minutes or until the water is absorbed and rice is tender. Remove from heat and let it sit covered for 5 minutes.
While the rice cooks, season the chicken thighs with salt and black pepper on both sides.
Heat the olive oil in a large skillet over medium-high heat. Add the chicken thighs skin-side down and cook for 6-7 minutes until the skin is golden brown and crispy. Flip the chicken and cook for another 5 minutes.
Remove the chicken thighs from the skillet and set aside on a plate.
In the same skillet, reduce heat to medium and add the minced garlic. Sauté for 1 minute until fragrant, stirring constantly to avoid burning.
Add the honey, soy sauce, apple cider vinegar, and red pepper flakes to the skillet. Stir well to combine and cook for 2 minutes until the sauce slightly thickens.
Return the chicken thighs to the skillet, spoon the sauce over them, cover, and simmer for 8-10 minutes until the chicken is cooked through (internal temperature of 165°F).
While the chicken simmers, steam the broccoli florets and sliced carrots in a steamer basket over boiling water for 5-7 minutes until tender but still crisp.
To serve, place a portion of cooked rice on each plate, top with two chicken thighs, spoon extra honey garlic sauce over the chicken, and arrange steamed broccoli and carrots on the side.