Pat the chicken breasts dry with paper towels and season them generously with salt and pepper on both sides.

In a small bowl, combine the minced garlic, chopped parsley, and thyme leaves. Rub this mixture all over the chicken breasts, pressing gently. Let the chicken rest at room temperature for 10 minutes.

Heat olive oil in a large skillet over medium-high heat until shimmering. Place the chicken breasts in the pan and sear without moving for 5-6 minutes until golden-brown. Flip and cook for another 5-6 minutes.

Add butter to the pan, basting the chicken with the melted butter and pan juices until the internal temperature reaches 165°F. Transfer the chicken to a plate and tent with foil.

In the same skillet with the drippings, add brown sugar and balsamic vinegar. Stir continuously over medium heat until the sugar dissolves and starts to caramelize, about 2 minutes. Pour in the chicken broth, scrape up any browned bits, and bring to a simmer. Cook for 5-7 minutes until the sauce reduces by half.

While the chicken cooks, peel and cut the potatoes into chunks. Cover with cold salted water in a large pot, boil, then simmer for 15-20 minutes until fork-tender. Drain, return to the pot, and mash with butter and heavy cream until smooth. Season with salt and pepper.

Spoon mashed potatoes onto each plate, place one chicken breast on top, drizzle with the reduced pan sauce, and garnish with fresh herbs. Serve immediately.