Pat chicken dry with paper towels. Season both sides generously with salt and pepper.

In a small bowl, combine minced garlic, chopped parsley, and thyme; rub over the chicken breasts and press it in. Let rest at room temperature for 10 minutes.

Heat 3 tablespoons olive oil in a large skillet over medium-high heat until shimmering.

Add the chicken and leave undisturbed for 5–6 minutes to form a deep golden crust.

Flip and cook another 5–6 minutes until chicken reaches an internal temperature of 165°F (74°C).

Add 2 tablespoons butter to the pan, tilting to pool the fat, and baste the chicken with melted butter and pan juices for 1–2 minutes.

Transfer chicken to a plate and tent with foil to rest.

Reduce heat to medium in the same skillet. Add 2 tablespoons brown sugar and 1 tablespoon balsamic vinegar; stir constantly for about 2 minutes until sugar dissolves and begins to caramelize.

Pour in 1 cup chicken broth and scrape up browned bits from the bottom with a wooden spoon. Simmer for 5–7 minutes until the sauce reduces by about half and becomes slightly syrupy. Taste and season with salt and pepper.

While chicken cooks, peel and cut russet potatoes into evenly sized chunks.

Place in a pot and cover with cold, salted water. Bring to a boil, reduce to a simmer and cook 15–20 minutes until fork-tender.

Drain well and return to the pot. Add butter and 1/2 cup heavy cream and mash until smooth and creamy. Season with salt and pepper.

Spoon a mound of mashed potatoes onto each plate, top with a chicken breast, and drizzle the reduced pan sauce over and around the chicken.

Garnish with extra parsley or thyme if desired. Serve immediately.