Add the potatoes to a pot of cold salted water. Bring to a boil and cook until fork-tender, about 15 minutes. Drain and let steam dry.
Preheat oven to 425°F. Toss carrots with olive oil, salt, and pepper. Roast for 25–35 minutes until tender. Melt butter with honey and grated garlic, then toss with roasted carrots.
Season chicken with salt, pepper, garlic, thyme, and herbs. Heat olive oil in a skillet and sear chicken 5–6 minutes per side until golden and cooked through. Remove and keep warm.
In the same skillet, sauté shallot and garlic. Add chicken stock, scraping browned bits. Simmer until slightly thickened, then whisk in cold butter for a silky sauce.
Mash potatoes. Warm butter, milk, and cream cheese, then mix into potatoes until smooth. Season to taste.
Serve Garlic Herb Chicken with Mashed Potatoes alongside glazed carrots and drizzle with pan sauce.