Whisk together 1/4 cup honey, 3 tablespoons Dijon mustard, 2 tablespoons whole grain mustard, and 2 minced garlic cloves in a large resealable bag or bowl until smooth.
Add the 4 small boneless, skinless chicken breasts to the bag and massage the marinade over the chicken until evenly coated; refrigerate for 4 to 24 hours.
Preheat the oven to 375°F (190°C).
On a large rimmed baking sheet, spread the halved Brussels sprouts and 1 pound sliced carrots in a single layer; drizzle with 2 tablespoons olive oil and season with salt and pepper, then toss to coat.
Place the marinated chicken breasts on the sheet pan among the vegetables, reserving any excess marinade in the bag (do not pour raw marinade over finished chicken unless boiled).
Bake in the preheated oven for about 25 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the vegetables are tender and lightly browned.
Remove from the oven and let the chicken rest a few minutes before serving.