Heat two of the tablespoons of oil in an oven safe cast iron skillet over medium low heat and add in the onions. Cook on medium low until they reach a dark amber colour, about one hour. Set aside.
Return the pan to the heat along with another tablespoon of oil. Add salt and pepper to the chicken breasts, and add to the pan. Pan fry on each side until golden brown but not cooked through, approximately four minutes per side. Remove from the pan and set aside.
Add in the garlic and cook for 30-60 seconds, then pour in the red wine and scrape the bottom of the pan. Add 3/4 cup of the low sodium beef broth, thyme, the cooked onions, herbs de province, and the browned chicken breasts. Cover and cook on medium low until the chicken breasts are cooked through, about another ten minutes.
Meanwhile, mix together the cornstarch with the remaining 1/4 cup of broth. Add to the pot and stir. Adjust the seasoning with more salt and pepper, to taste, if desired.
Preheat the broiler. Top the chicken with the two cheeses and broil until bubbly and golden brown. Serve with crusty whole grain bread.