French Onion Chicken

4 boneless skinless chicken cutlets, (16 to 20 ounces total)
2 teaspoons olive oil
2 medium yellow onions, thinly sliced
1 tablespoon balsamic vinegar, or more as needed
1 tablespoon Worcestershire sauce
½ teaspoon dried thyme or 1 teaspoon fresh thyme leaves
3 ounces Gruyère cheese, coarsely grated (about 1 cup)
½ cup all-purpose flour, or gluten-free flour mix*
1 teaspoon kosher salt
pepper, to taste
½ teaspoon paprika
2 teaspoons unsalted butter
1/2 cup chicken broth

In a large nonstick skillet heat the oil over medium heat.
Add the onions and 1/4 teaspoon salt, increase to medium-high, and cook, stirring frequently, until they start to brown around the edges.

Turn the heat to medium-low and add the balsamic vinegar, Worcestershire sauce, and thyme. Continue to cook, stirring occasionally, for 20 to 25 minutes, or until the onions are very tender. Add 1 to 2 tablespoons of water to deglaze. Set aside and wipe out the skillet.

Caramelized Onions
If the chicken is not uniformly thin, place it between two sheets of plastic wrap and pound with a meat tenderizer or the bottom of a heavy pan until thin but still intact. Season to taste with 1 teaspoon salt and black pepper and set aside.
In a wide, shallow bowl, whisk together the flour, pinch of salt, and paprika.
Set a large nonstick skillet over medium heat and melt 1 teaspoon butter.
Dredge two of the chicken cutlets in the seasoned flour, then shake off the excess and lay them side by side in the pan.

Cook the chicken for 3 minutes, or until lightly browned, then flip and cook for 3 more minutes. Set aside on a dish and repeat with the remaining butter and chicken. Set aside.

Combine the broth and 1 tablespoon of the flour mixture and mix, add it to the skillet and whisk on low heat, 1 minute, until it thickens. Toss the rest of the flour out.
Return the chicken to the skillet, top with onions and cheese and cover. Cook low 3 to 5 minutes, until the cheese is melted and bubbling.