Preheat oven to 425°F (220°C). Line a sheet pan with foil for easier cleanup.
Whisk honey, soy sauce, oil, garlic, vinegar, and mustard. Season with salt, pepper, and red pepper flakes if using.
Toss potatoes and vegetables with a little oil, salt, and pepper; spread on the sheet pan. Nestle chicken thighs skin-side up among the veggies.
Brush or pour half the honey-garlic sauce over chicken and veggies. Roast 30–35 minutes until chicken reaches 165°F and veggies are tender.
Broil 2–3 minutes if you want extra crispy skin, watching closely. Drizzle remaining sauce over everything before serving and sprinkle parsley.