Place peeled and quartered potatoes in a large pot and cover with cold water. Add a generous pinch of salt and bring to a boil. Reduce heat to medium and simmer for 15-20 minutes until potatoes are fork-tender. Drain well and return to the warm pot. Add warm milk, butter, and sour cream. Mash until smooth and creamy. Season with salt to taste and keep warm.

Pat chicken breasts dry with paper towels and season both sides with salt and pepper. In a large skillet, heat olive oil over medium-high heat. Add chicken and cook for 5-6 minutes per side until golden brown and cooked through (internal temperature 165°F). Remove chicken from skillet and set aside.

Reduce heat to medium and add butter to the same skillet. Add minced garlic and cook for 30 seconds until fragrant. Stir in fresh herbs and honey, then return chicken to the skillet. Spoon the garlic herb butter over the chicken for 1-2 minutes to create a beautiful glaze.

Remove chicken from skillet and set aside. Sprinkle flour into the skillet and cook for 1 minute, stirring constantly. Gradually whisk in chicken broth, scraping up any browned bits from the bottom of the pan. Stir in heavy cream and simmer until sauce thickens slightly. Stir in remaining butter until melted and glossy.

Spoon creamy mashed potatoes onto plates, top with glazed chicken breasts, and drizzle with the rich pan sauce. Garnish with fresh herbs and serve immediately.