Preheat the oven to 400°F. In a small bowl, mix together olive oil, minced garlic, thyme, rosemary, salt, and black pepper. Rub the mixture all over the chicken breasts.
Place the seasoned chicken breasts in a baking dish and bake for 25-30 minutes or until the internal temperature reaches 165°F. Remove from the oven and let rest for 5 minutes before slicing.
While the chicken is baking, bring a large pot of salted water to a boil. Add the cubed potatoes and cook for 15-20 minutes or until tender. Drain and return to the pot.
Add milk and butter to the potatoes. Mash until smooth and creamy. Season with salt and pepper to taste.
In a medium saucepan, combine sliced carrots, brown sugar, and water. Bring to a boil, then reduce heat to a simmer. Cook for 10-15 minutes or until the carrots are tender and the liquid has thickened slightly.
Serve the sliced garlic herb chicken alongside the creamy mashed potatoes and glazed carrots.