In a small bowl, whisk together honey and mustard.
Wash the chicken thighs and pat dry.
Season thighs on both sides liberally with salt and pepper.
In a large skillet over medium-high heat, add two tablespoons of olive oil. Sear the thighs, skin side down until golden brown, about 5 minutes. Flip the thighs and cook the other side for another 3 minutes.
Transfer the browned chicken to a large plate and set aside.
In the same skillet, add the remaining olive oil and garlic. Cook the garlic until fragrant then add the potatoes and carrots. Season with salt and pepper. Continue cooking for another 15 minutes.
Place the vegetables in a roasting pan. Arrange the thighs skin side up on top of the vegetables. Lather the chicken pieces with the honey mustard sauce.
Transfer the baking dish to the oven and roast the chicken for another 50-60 minutes.
Remove from the oven and let it cool for 10 minutes before serving.