Pat the chicken breasts dry and season them well with salt and pepper on both sides.
In a bowl, mix minced garlic, chopped parsley, and thyme leaves and rub the blend all over the chicken, pressing lightly to coat.
Allow the chicken to sit at room temperature for 10 minutes so the herbs soak in.
Heat olive oil in a large skillet on medium-high heat until it shimmers.
Place the chicken in the skillet carefully and sear it without moving for about 5 to 6 minutes until golden and crisp.
Flip the chicken and cook the other side for the same amount of time.
Add butter to the pan and spoon the melted butter over the chicken frequently to baste it.
Once the chicken reaches an internal temp of 165°F, remove it from the pan, place on a plate, and cover loosely with foil.
In the same pan, add brown sugar and balsamic vinegar, stirring continuously over medium heat until the sugar melts and starts to caramelize, around 2 minutes.
Pour chicken broth into the skillet, scraping the bottom to loosen any browned bits.
Let the sauce simmer for 5 to 7 minutes until it thickens and reduces by about half.
Season the sauce with salt and pepper to taste.
Meanwhile, peel and chop potatoes into even pieces then place them in a pot and cover with cold salted water.
Bring the water to a boil, then reduce to a simmer and cook the potatoes until fork-tender, about 15 to 20 minutes.
Drain the potatoes and return them to the pot.
Add butter and heavy cream and mash until smooth and creamy.
Season the mashed potatoes with salt and pepper as desired.
To serve, spoon mashed potatoes onto plates creating a bed and place a chicken breast on top.
Generously drizzle the prepared pan sauce over the chicken and around the plate.
Garnish with extra fresh herbs if preferred and serve right away while warm.
