Preheat the oven to 400°F (200°C) and line a large sheet pan with parchment paper.
In a bowl, mix honey, mustard, olive oil, garlic, salt, pepper, and paprika until smooth.
Pat chicken dry and place it on one side of the sheet pan. Add potatoes, carrots, and broccoli around it.
Pour the sauce over the chicken and vegetables. Toss vegetables lightly to coat and spread everything evenly.
Bake for 30 to 40 minutes, flipping vegetables halfway through cooking, until chicken is fully cooked and vegetables are tender and slightly crispy.
Remove from oven and let rest for 5 minutes before serving. Spoon extra sauce over the top if desired.