Preheat the oven to 400°F (200°C).
Season the chicken thighs evenly with salt and black pepper on both sides.
Heat olive oil in a large oven-safe skillet over medium-high heat.
Place the chicken thighs skin-side down in the skillet and cook for 5-7 minutes until the skin is golden brown and crispy. Flip and cook for an additional 3 minutes.
Remove the chicken thighs from the skillet and set aside.
In the same skillet, reduce heat to medium and add the minced garlic. Sauté for 1 minute until fragrant.
Add honey, soy sauce, apple cider vinegar, and crushed red pepper flakes to the skillet. Stir to combine and bring the sauce to a simmer.
In a small bowl, mix cornstarch and water until smooth. Slowly pour the mixture into the sauce while stirring continuously to thicken it. Cook for 1-2 minutes until the sauce thickens.
Return the chicken thighs to the skillet, spoon some sauce over them, and transfer the skillet to the preheated oven.
Bake for 15 minutes or until the chicken reaches an internal temperature of 165°F (74°C).
While the chicken is baking, rinse the rice under cold water until the water runs clear.
In a medium saucepan, bring 3 cups of water to a boil. Add the rice, reduce heat to low, cover, and simmer for 15 minutes or until the water is absorbed and rice is tender.
Steam the broccoli florets and sliced carrots until tender but still crisp, about 5-7 minutes.
Remove the chicken from the oven and let it rest for 5 minutes.
Serve the honey garlic chicken thighs over the cooked rice with steamed broccoli and carrots on the side. Spoon extra sauce from the skillet over the chicken and vegetables.