Preheat your oven to 400°F (200°C) and prepare a large rimmed baking sheet. Wash all of the vegetables thoroughly before chopping them into evenly sized pieces to ensure they cook at the same rate.
In a medium mixing bowl, whisk together the mayonnaise, Dijon mustard, yellow mustard, honey, apple cider vinegar, garlic powder, paprika, ¼ teaspoon salt, and ¼ teaspoon black pepper until the sauce is smooth and creamy.
Add the chicken thighs to the bowl and turn them several times until every piece is fully coated with the honey mustard mixture. Set aside while preparing the vegetables.
Spread the cubed potatoes, diced red onion, chopped carrots, and trimmed green beans evenly across the sheet pan. Drizzle the vegetables with vegetable oil, then season with the remaining salt and black pepper. Toss everything together until evenly coated and arrange the vegetables into a single layer.
Place the coated chicken thighs directly on top of the vegetables. Spoon any remaining honey mustard sauce over each piece of chicken to maximize flavor.
Bake the Sheet Pan Honey Mustard Chicken and Veggies for 25 to 30 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the potatoes are fork tender.
For a deeper golden color and slightly caramelized glaze, switch the oven to broil for the final 2 to 3 minutes, watching carefully to prevent burning.
Remove the pan from the oven and allow the chicken to rest for about 5 minutes before serving. Garnish with chopped fresh parsley if desired.