Preheat oven to 350-degrees Fahrenheit.
Season the chicken thighs with 1 teaspoon salt and ¼ teaspoon pepper. Set aside.
Melt the butter in a large skillet over medium heat. Add the sliced onions and increase the heat to medium/high, stirring occasionally.
Add the remaining salt, pepper and 1 teaspoon dried thyme. Continue to cook and stir the onions until they develop a deep golden color (approximately 20 minutes).
Add the garlic, beef broth, and white wine. Continue to cook until the onions thicken and the liquid evaporates.
Spoon the onions evenly into a 9" x 13" casserole dish that has been sprayed with cooking spray.
Carefully wipe the skillet with paper towels.
Heat the oil in the skillet to medium and add the bread, sliced side down. Cook the bread in the skillet until crisp and browned, being careful to keep an eye on them as they can burn quickly.
Remove the browned bread from the skillet using tongs and place the browned bread, cut side up on the caramelized onions.
Place one chicken thigh on top of each slice of bread.
Bake in a preheated oven for 35 minutes.
Remove the casserole dish from the oven and brush each thigh with the balsamic vinegar.
Place the shredded cheese evenly over each chicken thigh and sprinkle the top of each thigh with the remaining dried thyme.
Return the chicken back into the oven for an additional 10 minutes to melt and brown the cheese.
To serve, make sure to spoon some of the onions along with each piece of bread and chicken thigh.