Slice the onions root to tip in half, and then slice half-moon shapes.
Heat the oil in a large skillet over medium heat, and then add the chicken cutlets to the hot pan, sprinkling the exposed side with salt and pepper.
Let cool for 3-4 minutes, until they release from the pan and are nicely browned, then flip and sear the other side.
Remove the chicken cutlets from the pan to a plate and set aside.
Add the butter to the pan, followed by the sliced onions, sugar, salt and thyme leaves.
Cook the onions, stirring every 4-5 minutes until golden brown, about 30-35 minutes.
Lower the heat if they threaten to burn, and place a lid on the pan to make them cook faster.
Once the onions are golden brown, add the white wine and lower the heat. Cook for 2-3 minutes.
Stir in the beef broth and lower the heat to a simmer.
Add the chicken back to the pan and simmer until the chicken is cooked through, another few minutes.
Just before serving, toast the bread and melt the cheese on top under a broiler.
Serve each chicken cutlet with a scoop of caramelized onions on top of the cheesy bread slices.