Boil potatoes: Start by boiling salted water in a large pot. Add peeled and cubed potatoes, cooking until fork-tender, about 15-20 minutes. Drain and mash with butter, milk (or cream), and salt to taste. Keep warm.

Glaze carrots: In a saucepan, combine sliced carrots, butter, brown sugar, salt, and water. Cover and simmer for 10-12 minutes until tender and glossy. Uncover for the last few minutes to thicken the glaze.

Prepare chicken: Pat the chicken dry and season with salt, pepper, garlic powder, thyme, and rosemary, coating each piece thoroughly.

Sear chicken: Heat olive oil and butter in a skillet over medium-high heat. Add chicken, searing for 4-5 minutes on each side until golden brown and cooked through. Remove and set aside.

Make the sauce: In the same skillet, add minced garlic and sauté until fragrant. Pour in chicken broth, scraping the bottom to deglaze. Stir in cream, Parmesan cheese, and Dijon mustard, simmering until slightly thickened, about 3-5 minutes.

Combine chicken and sauce: Return the cooked chicken to the skillet, spooning sauce over it. Simmer together for about 2 minutes to soak in the flavors.

Serve: Plate fluffy mashed potatoes next to glazed carrots, drizzling extra sauce over both chicken and potatoes. Garnish with fresh parsley or chives.