Heat 2 tablespoons of oil in a nonstick skillet over medium low heat and add in the onions. Cook on medium low until they reach a dark amber colour, about 1 hour. Set aside.
Return the pan to the heat along with another tablespoon of oil. Sprinkle the chicken breasts with salt and pepper and add to the pan. Pan fry on each side until golden brown, about 4 minutes per side. Remove from the pan and set aside.
Add in the garlic and stir until fragrant, then pour in the red wine and scrape up the bottom of the pan. Add 3/4 cup of beef broth, herbs de province, thyme, cooked onions and the browned chicken breasts. Cover and cook on medium low until the chicken breasts are cooked through, about another 10 minutes.
Mix together the cornstarch with the remaining 1/4 cup of broth. Add to the pot and stir. Season with salt and pepper, to taste.
Meanwhile, preheat the broiler. Top the chicken with the gruyere and parmesan and broil until bubbly and golden brown. Enjoy.