Preheat oven to 375F, grease or line a 9x13 baking dish.
In a bowl, combine mayonnaise, cheese, and seasonings.
Coat the chicken:
Place chicken breasts on the baking dish. Distribute the mixture over the chicken, making sure to coat all the tops.
Bake:
Place carrots and Brussels sprouts on a baking tray, drizzle olive oil, and season with salt. Bake the veggies in the preheated oven for 30 minutes.
Bake chicken breasts for 45 minutes until the internal temperature reaches 165F. Remove from the oven and allow to rest 5-10 minutes before serving with the vegetables.
Notes
If you want to cut down on the fat, you can use ½ cup mayonnaise with ½ cup plain Greek yogurt. The yogurt also can help the chicken retain moisture, and it adds a tangy flavor.