Preheat the oven to 400°F (200°C).
In a bowl, mix balsamic vinegar, honey, olive oil, minced garlic, and season with salt and pepper. Add chicken thighs, ensuring they are well-coated. Marinate for 10 minutes if time allows.
While the chicken is marinating, prepare the potatoes. Place the cubed potatoes in a large pot, cover with water, and bring to a boil. Cook until tender, about 15-20 minutes. Drain and return to the pot.
For the mashed potatoes, add milk, goat cheese, butter, salt, and pepper to the drained potatoes. Mash until smooth and creamy. Set aside, keeping warm.
While the potatoes are boiling, prepare the carrots. Spread the carrot sticks on a baking sheet, drizzle with olive oil, and season with salt and pepper. Roast in the preheated oven for about 25 minutes, or until tender and slightly caramelized.
In a frying pan, heat a little olive oil over medium-high heat. Add the marinated chicken thighs, skin-side down. Sear for about 5-7 minutes until golden brown. Flip and cook for another 5 minutes.
Transfer the seared chicken thighs to the oven, placing them on a baking sheet. Bake for about 20-25 minutes, or until the internal temperature reaches 165°F (74°C).
Serve the chicken thighs alongside goat cheese mashed potatoes and roasted carrots. Garnish with fresh herbs if desired.