Whisk the honey, Dijon mustard, whole grain mustard, and minced garlic together in a large bowl or combine in a large resealable bag until smooth.
Add the chicken breasts to the bag, seal, and massage the marinade over the chicken to coat evenly; 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 carrot rounds in a single layer; drizzle with olive oil and season with salt and pepper, then toss to coat.
Arrange the marinated chicken breasts on the sheet pan among the vegetables.
Bake for about 25 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the vegetables are tender.
Remove from the oven and let the chicken rest a few minutes before serving.