Heat the oven - Preheat the oven to 425°F.
Season vegetables - Add carrots, potatoes, onions, and rosemary to a 9x13 baking dish, and season with kosher salt and freshly cracked black pepper. In a small mixing bowl, whisk 3 tablespoons olive oil, honey, and whole grain mustard. Pour over vegetable mixture and mix until the vegetables are coated.
Prepare chicken - Pat the chicken thighs dry with a paper towel. Arrange the chicken thighs on top of the vegetables. Lift the skin of each chicken thigh and tuck 1 pat of butter under each skin.
Season chicken - Coat the chicken thighs in remaining 3 tablespoons of olive oil and rub into the thighs. Season each thigh with kosher salt and black pepper.
Bake chicken - Bake covered for 30 minutes, remove the cover, then bake for an additional 30-40 minutes, or until the skin is golden and the internal temperature of the chicken is 165°F.
Serve - Remove from the oven and allow to rest for 10 minutes, then serve. Spoon juices over each serving.
