Preheat your oven to 400°F (200°C).
In a mixing bowl, whisk together honey, balsamic vinegar, olive oil, garlic powder, salt, and pepper. Add the chicken thighs and coat them well in the marinade. Let them marinate while preparing the other components.
On a baking sheet, spread the chopped carrots in an even layer. Drizzle with olive oil, salt, pepper, and thyme if using. Toss to coat evenly. Roast in the preheated oven for about 20 minutes.
After the carrots have roasted for 20 minutes, place the marinated chicken thighs on the same baking sheet (skin side up) and return to the oven. Roast for an additional 25 to 30 minutes, or until the chicken reaches an internal temperature of 165°F (75°C).
While the chicken and carrots are cooking, place the chopped potatoes in a large pot and cover with water. Bring to a boil and cook until fork-tender, about 15-20 minutes. Drain the potatoes and return them to the pot.
Add goat cheese, milk, butter, and salt and pepper to the cooked potatoes. Mash until smooth and creamy. Adjust seasoning to taste.
Once everything is done cooking, remove the chicken thighs and carrots from the oven. Let the chicken rest for a few minutes before serving.
Serve the honey balsamic chicken thighs with a generous scoop of goat cheese mashed potatoes and roasted carrots on the side.