Begin by placing the peeled and chopped Yukon Gold or Russet potatoes in a large pot. Cover them with cold water by about 1 inch and stir in 1 ½ teaspoon kosher salt. Bring the water to a boil over medium-high heat, then reduce to a gentle boil. Cook the potatoes for about 15–20 minutes, or until they are very tender. Drain well and let them sit in the pot for 1–2 minutes to steam off excess moisture.
While the potatoes are steaming, warm the milk in a small saucepan over low heat. Add 4 tablespoon of room temperature unsalted butter to the hot potatoes and mash until mostly smooth. Gradually stir in the warm milk and, if desired, sour cream or cream cheese for added creaminess. Season with ½ teaspoon kosher salt and ¼ teaspoon freshly ground black pepper, mixing until well combined, and adjust the seasoning to taste.
While the potatoes are cooking, prepare the chicken breasts. Pat them dry with paper towels and season both sides generously with a mixture of 1 teaspoon kosher salt, ½ teaspoon black pepper, garlic powder, and onion powder. This will help enhance the flavors of the creamy herb chicken as it cooks. Let the chicken sit for a few minutes to allow the seasoning to penetrate.
In a large skillet over medium-high heat, heat 2 tablespoon of olive oil and 1 tablespoon of unsalted butter. Once hot, add the seasoned chicken breasts in a single layer, making sure not to overcrowd the pan. Sear the chicken for 4–5 minutes on each side, or until golden and the internal temperature reaches about 68–70 °C (155–160 °F). Transfer the chicken to a plate and cover loosely with foil to keep warm.
In a medium skillet, combine the sliced carrots with 2 tablespoon of unsalted butter, 2 tablespoon of brown sugar or honey, and ¼ cup of water or orange juice. Season with ¼ teaspoon kosher salt and ⅛ teaspoon black pepper. Bring the mixture to a simmer over medium heat, cover, and cook for 6–8 minutes or until the carrots are just tender. Remove the lid and continue cooking for another 3–5 minutes, allowing the liquid to reduce into a glossy glaze. Stir in fresh lemon juice if using.
Using the same skillet from the chicken, reduce the heat to medium and melt the remaining 1 tablespoon of butter. Add the finely minced shallot and cook until translucent, followed by the minced garlic until fragrant. Pour in ½ cup of dry white wine and simmer until reduced by half. Stir in 1 cup of chicken broth, 1 cup of heavy cream, 1 teaspoon Dijon mustard and the remaining black pepper, simmering until the sauce slightly thickens.
Return the seared chicken breasts to the skillet, spooning the creamy herb sauce over each piece. Simmer for an additional 4–6 minutes, ensuring the chicken reaches an internal temperature of 74 °C (165 °F). Allow the chicken to rest in the sauce for 3–5 minutes, soaking in all those wonderful flavors.
Give the mashed potatoes a final stir, then spoon them onto each plate. Place a chicken breast alongside or on top of the potatoes, garnishing with a generous ladle of the creamy herb sauce. Add the glossy glazed carrots to the plate, and if desired, sprinkle with freshly chopped herbs for an inviting touch.