Pat the chicken breasts dry using paper towels, then season both sides with salt and pepper. In a small bowl, combine minced garlic, chopped parsley, and fresh thyme, and rub this mixture all over the chicken. Let the chicken rest for 10 minutes.

Heat a large skillet over medium-high heat and add a tablespoon of olive oil. Once the oil shimmers, place the seasoned chicken breasts in the skillet. Sear for 5-6 minutes on one side until golden brown. Flip the chicken, adding a pat of butter, and baste as it cooks for another 5-6 minutes until it reaches an internal temperature of 165°F.

Remove the chicken from the skillet and cover loosely with foil. In the same skillet, reduce heat to medium and add brown sugar and balsamic vinegar. Stir continuously for 2-3 minutes until the sugar dissolves and begins to caramelize.

Pour in chicken broth, scraping the skillet to release flavorful bits. Bring to a simmer and let reduce for 5-7 minutes until slightly thickened. Adjust seasoning as needed.

Peel and cube russet potatoes. Boil in salted water for 15-20 minutes until fork-tender. Drain and return to the pot. Add butter and heavy cream, mashing until creamy. Season with salt and pepper.

Spoon a portion of mashed potatoes onto each plate. Place a chicken breast on top and drizzle with warm pan sauce. Garnish with freshly chopped herbs if desired.