Preheat the oven to 425°F (220°C).
In a large mixing bowl, whisk together honey, balsamic vinegar, olive oil, minced garlic, salt, pepper, and thyme. Add the chicken thighs and coat them well with the marinade. Let it marinate for at least 10 minutes while you prepare the other ingredients.
For the roasted carrots, place the sliced carrots on a baking sheet. Drizzle with olive oil and honey, then sprinkle with salt and pepper. Toss to coat evenly and set aside.
Place the marinated chicken thighs on another baking sheet skin-side up. Put both the chicken and the carrots in the oven and roast for 25-30 minutes, or until the chicken is cooked through and has an internal temperature of 165°F (74°C) and the carrots are tender and beginning to caramelize.
While the chicken and carrots are roasting, prepare the goat cheese mashed potatoes. In a medium saucepan, add peeled and cubed potatoes and cover with water. Bring to a boil and cook until tender, about 15-20 minutes.
Drain the potatoes and return them to the saucepan. Add in goat cheese, milk, and butter. Mash the potatoes until creamy. Season with salt and pepper to taste.
Once the chicken and carrots are done, remove them from the oven. Serve the honey balsamic chicken thighs with a generous portion of goat cheese mashed potatoes and roasted carrots on the side.