Preheat the oven to 400°F (200°C).
Season the chicken thighs evenly with salt and black pepper on both sides.
Heat the olive oil in a large oven-safe skillet over medium-high heat.
Add the chicken thighs skin-side down and sear for 5-6 minutes until the skin is golden brown and crispy. Flip and cook for an additional 3 minutes. Remove chicken from the skillet and set aside.
In the same skillet, reduce heat to medium and add the minced garlic. Sauté for 30 seconds until fragrant.
Add the honey, soy sauce, apple cider vinegar, dried thyme, and crushed red pepper flakes to the skillet. Stir to combine and cook for 2 minutes until the sauce slightly thickens.
Return the chicken thighs to the skillet, spooning some sauce over them.
Add the broccoli florets and sliced carrots around the chicken in the skillet.
Transfer the skillet to the preheated oven and bake for 20 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the vegetables are tender.
While the chicken is baking, rinse the rice under cold water until the water runs clear.
In a medium saucepan, bring 2 cups of water to a boil. Add the rinsed rice and a pinch of salt, reduce heat to low, cover, and simmer for 15 minutes or until the water is absorbed and rice is tender.
Remove the saucepan from heat and stir in the unsalted butter. Fluff the rice with a fork.
Remove the skillet from the oven. Spoon the honey garlic sauce over the chicken and vegetables.
Serve the honey garlic chicken thighs with the roasted vegetables and buttered rice on the side.