Preheat the oven to 425°F (220°C). Line a large baking sheet with parchment paper.
Place the potatoes, carrots, and red onion on the prepared baking sheet.
Drizzle the vegetables with olive oil and season with salt, pepper, and fresh thyme. Toss until evenly coated.
Roast the vegetables for 15 minutes.
While the vegetables cook, season the chicken thighs and drumsticks generously with salt and pepper on both sides.
Remove the baking sheet from the oven and gently stir the vegetables.
Arrange the chicken pieces around the vegetables in a single layer.
Return the pan to the oven and bake for another 15 minutes.
In a small bowl, whisk together Dijon mustard, whole-grain mustard, honey, brown sugar, salt, and pepper until smooth.
Remove the pan from the oven and drizzle the honey mustard sauce evenly over the chicken and vegetables.
Return the pan to the oven and continue baking for 20–25 minutes, or until the chicken reaches an internal temperature of 165°F (74°C).
Let the One Pan Honey Mustard Chicken and Veggies rest for a few minutes before serving.