1)In a large nonstick skillet heat the oil over medium heat.

2)Add the onions and 1/4 teaspoon salt, increase to medium-high, and cook, stirring frequently, until they start to brown around the edges.

3)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.

4)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.

5)In a wide, shallow bowl, whisk together the flour, pinch of salt, and paprika.

6)Set a large nonstick skillet over medium heat and melt 1 teaspoon butter.

7)Dredge two of the chicken cutlets in the seasoned flour, then shake off the excess and lay them side by side in the pan.

8)Cook the chicken for 3 minutes, or until lightly browned, then flip and cook for3 more minutes. Set aside on a dish and repeat with the remaining butter and chicken. Set aside.

9)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.

10)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.