Preheat oven to 425°F. Toss carrots with 1 tbsp oil, salt, and pepper on a sheet pan; spread in one layer.
Whisk mustard, honey, remaining oil, vinegar, garlic powder, paprika, salt, and pepper in a bowl.
Pat chicken dry, season lightly, then brush or toss with half the honey-mustard.
Arrange chicken on the sheet pan with carrots and roast 18–22 minutes, brushing with more sauce halfway, until chicken reaches 165°F.
Broil 1–2 minutes if you want caramelized edges. Let rest 5 minutes; sprinkle parsley.