Peel the onions and cut in half on the root or stem end. Then start slicing no more than 1/4" slices. This will give you half rings.

Place 2 tablespoons olive oil in pan and heat to medium-low. Add onions and cook until the onions are a deep rich brown color. About 45 minutes. Don't turn up the heat. Watch closely, you do not want to burn them, but they will be very brown and reduce down to less than half of their original volume.

While the onions are cooking, put another large skillet* on high heat. Add 1 tablespoon of olive oil. Season the chicken with salt and pepper than brown the each side of the chicken for 5 mins per side. Remove the chicken from the pan and place in 9x13 glass pyrex.*

Once the onions have caramelized, add garlic, thyme and flour to onions and stir until flour is absorbed. Continue to cook for 3 minutes. Then add the wine and deglaze. Add the chicken broth and continue to scrape up any bits on the bottom of the pan. Add the balsamic vinegar, mustard and Worcestershire sauce and bring to a boil. (Add any deglazed juices from cooking the chicken.) The sauce should start to thicken in a few minutes, turn off heat.

Pour the sauce over the chicken and bake in a preheated 350° oven for 20 minutes. Then remove from the oven and turn the oven to broil. Cover each thigh with a generous portion of the shredded Swiss cheese. Place pan back in the oven and broil until cheese is melted and golden brown. (about 5 minutes depending on your oven)

Serve over spaghetti or noodles.