Boil potatoes until tender (15–20 mins). Mash with warm cream, butter, and salt.
Season chicken and sear in skillet with oil + butter (4–5 mins/side). Set aside.
In same skillet, add butter + olive oil. Cook onions with a good pinch of salt on medium low heat for 20 mins. Add balsamic + thyme and cook 18–20 more mins until caramelized.
Add garlic, cook 1 min. Stir in flour, then broth + Worcestershire. Simmer 2–3 mins to thicken.
Add chicken back, spoon sauce over, sprinkle Gruyère, cover to melt. Garnish with parsley.
Serve chicken and onion sauce over mashed potatoes.
