Preheat oven to 425°F and line a large sheet pan with parchment paper or aluminum foil.
In a medium bowl, whisk together honey, Dijon mustard, whole grain mustard, 2 tablespoons olive oil, minced garlic, thyme, salt, and pepper.
Place chicken pieces in a bowl and toss with half of the honey mustard sauce. Set aside the remaining sauce.
Toss carrots and green beans with remaining 1 tablespoon olive oil and a pinch of salt.
Arrange vegetables on one side of the sheet pan and chicken pieces on the other side.
Bake for 15 minutes, then brush chicken with half of the reserved honey mustard sauce. Stir the vegetables.
Continue baking for 10 more minutes until chicken is cooked through (internal temperature of 165°F) and vegetables are tender.
Drizzle with remaining honey mustard sauce, garnish with fresh parsley, and serve immediately!