Season both sides of the chicken breasts with salt and pepper. In a heavy bottom soup pot, Dutch oven or braiser (as in video) over medium low heat add the oil. Brown the chicken on both sides. Remove from pan, cover and set aside.
To the same pot, add the butter and sliced onions, tossing to coat. Add the salt and red pepper flakes. Cover with lid and cook for 15 minutes. Remove lid and turn heat to low. Cook, stirring often, another 5 minutes until onions are a dark golden brown. Add the flour and cook another minute. Carefully pour in the beef stock and thyme. Stir to mix and sauce will thicken.
Add cooked chicken and juices back into the pan, turning to coat with onion mixture. Top each chicken breast with 2 slices of cheese, cover and cook for 5 minutes.
Serve with chopped chives and spoon onions with sauce on top.