Heat Oven: Preheat the oven to 450°F. Line a half sheet pan with parchment paper or foil if you want easier cleanup.
Prep Vegetables: Add the Brussels sprouts and carrots to the sheet pan.
1 pound Brussels sprouts, 1 pound carrots
Oil and Season Veggies: Drizzle the vegetables with 2 tablespoons oil, then season generously with salt and pepper. Toss right on the pan and spread into an even layer so they roast, not steam.
Salt, Black pepper, 3 tablespoons cooking oil
Even Out the Chicken: If the chicken breasts are thick, pound them to an even thickness (about ¾-inch) so they cook evenly and stay juicy.
4 boneless
Add and Season Chicken: Nestle the chicken breasts between the vegetables. Drizzle the tops with the remaining 1 tablespoon oil and season with salt and pepper.
First Roast: Roast for 15 minutes to get everything started and begin browning.
Make the Honey Dijon Sauce: While the pan roasts, whisk together the mayonnaise, honey, and Dijon mustard until smooth. Divide the sauce into two bowls—one for glazing, one for dipping.
2 tablespoons mayonnaise, 3 tablespoons honey, 3 tablespoons Dijon mustard
Flip Veggies: Remove the sheet pan from the oven and use a spatula to turn the vegetables so they brown evenly.
Glaze the Chicken: Brush the tops of the chicken breasts with the first bowl of honey Dijon sauce, coating them well. Keep the second bowl for serving.
Finish Roasting: Return the pan to the oven and roast 8 to 15 minutes more, until the chicken reaches 165°F in the thickest part and the vegetables are tender. If the chicken finishes before the veggies, transfer the chicken to a plate to rest and keep roasting the vegetables for 5 to 8 minutes.
Rest and Serve: Let the chicken rest for 5 minutes, then serve with the roasted vegetables and the reserved honey Dijon sauce for dipping.