Preheat the oven to 425°F (220°C).
In a mixing bowl, whisk together the honey, balsamic vinegar, olive oil, minced garlic, salt, and pepper.
Place the chicken thighs in a large skillet over medium-high heat and sear them for 4-5 minutes on each side until browned.
Transfer the seared chicken thighs to a baking sheet and brush them generously with the honey balsamic mixture. Bake in the preheated oven for 25-30 minutes, or until the internal temperature reaches 165°F (74°C).
While the chicken is baking, boil the cubed potatoes in salted water until tender for approximately 15-20 minutes.
Drain the water from the potatoes, then return them to the pot.
Add goat cheese, heavy cream, butter, salt, and pepper to the potatoes. Mash until smooth and creamy. Adjust seasoning if necessary.
Toss the carrot sticks with olive oil, salt, pepper, and thyme (if using) on a separate baking sheet. Roast in the oven for about 20-25 minutes, or until tender and slightly caramelized.
Once everything is cooked, serve the honey balsamic chicken thighs with a side of goat cheese mashed potatoes and roasted carrots.