Marinate the chicken by whisking honey, balsamic vinegar, olive oil, Dijon mustard, salt, and pepper in a mixing bowl. Score chicken thighs' skin and coat them in marinade. Refrigerate for at least 30 minutes.

Prepare Yukon Gold potatoes by rinsing, scoring the skins, boiling in salted water for 20-30 minutes until fork-tender, then cool slightly before peeling.

Preheat the oven to 350°F (175°C).

Arrange marinated chicken skin-side up on a foil-lined baking sheet. Let sit at room temperature for about 10 minutes.

Prepare carrots by peeling and cutting into uniform pieces, tossing with olive oil, honey, balsamic vinegar, salt, and pepper. Spread in a baking dish.

Bake chicken and carrots in the preheated oven for 35-45 minutes, until chicken is 160°F internal temperature and skin is golden.

Heat whole milk and butter in a saucepan with minced garlic and thyme over low heat for 5-7 minutes. Strain.

Mash cooled potatoes, adding infused milk/butter mixture and goat cheese, mixing until creamy. Season with salt and pepper.

Prepare the glaze by simmering balsamic vinegar, honey, and optional orange juice in a saucepan for 5-7 minutes until thickened. Stir in butter.

Serve the chicken and potatoes topped with the balsamic glaze and alongside the roasted carrots.