Place the peeled and chopped potatoes into a pot filled with cold salted water. Bring to a boil and cook until a fork slides in easily, around 15 minutes. Drain the water and return the potatoes to the pot, allowing them to steam for a couple of minutes before covering and setting aside.

Heat the oven to 425°F. On a parchment-lined baking sheet, toss the carrots with 1 tablespoon of olive oil, salt, and pepper. Roast them for 25 to 35 minutes until tender and slightly caramelized. Towards the end, combine 2 tablespoons butter, honey, and grated garlic in a small pan, melting until fragrant and bubbling. Drizzle this glaze over the hot carrots and mix well.

Dry the chicken breasts thoroughly, then season with salt, pepper, half the minced garlic, thyme, and Italian herbs, massaging in 1 tablespoon of olive oil. In a large skillet over medium-high heat, heat the remaining 2 tablespoons of olive oil. Sear the chicken for about 5 to 6 minutes per side until golden and cooked through. Remove and cover with foil to keep warm.

In the same skillet, sauté the minced shallot and remaining garlic for 1 to 2 minutes over medium heat. Pour in the white wine to deglaze the pan, scraping up browned bits. Let it simmer for 2 to 3 minutes, then add the chicken stock and keep simmering until the sauce thickens slightly. Remove from heat and whisk in the cold butter until the sauce is smooth and glossy. Adjust seasoning with salt and pepper.

Mash the hot potatoes to your desired texture. Warm the butter, cream cheese, and milk together until combined, then stir this mixture into the potatoes to achieve creamy mashed potatoes. Season with salt and pepper to taste.