8 thin-sliced skinless, boneless chicken breast cutlets (about 1 1/2 pounds)

12 slices from a package of sliced Swiss cheese, 4 slices torn into pieces (about 1/2 pound total)

4 slices from a package of deli-style ham

1/2 C. plus 2 T. all-purpose flour

1 tsp. paprika

Salt and freshly ground black pepper

4 T. unsalted butter

1 T. extra-virgin olive oil

3 T. dry vermouth or white wine (optional)

1 C. heavy cream or whole milk

 

On a work surface, make sandwiches using 2 of the chicken breast cutlets for each: layer 1 of the cutlets, a slice of Swiss cheese and a slice of ham, then another slice of cheese and a slice of chicken. Fasten the sandwiches in the center with a toothpick. On a plate, mix the 1/2 C. of flour with the paprika and season with 1/2 tsp. of salt and 1/4 tsp. of pepper. Dredge a sandwich in the flour to coat lightly on both sides, shaking off any excess. Repeat with the remaining sandwiches. In a 12-inch skillet, melt 2 T. of the butter in the olive oil and cook the sandwiches over medium-high heat until cooked through and golden, turning once, about 3 minutes per side. Meanwhile, in a medium saucepan, melt the remaining 2 T. of butter over medium heat. Whisk in the remaining 2 T. of flour until smooth. Whisk in the vermouth and cook for 1 minute (optional). Slowly whisk in the heavy cream and cook, stirring continuously, until the sauce comes to a soft boil and thickens, about 5 minutes. Stir in the torn up Swiss cheese and cook over low heat, stirring continuously, until the cheese is melted, 2 to 3 minutes. Season the sauce with salt and pepper and serve the fondue-style sauce in small bowls alongside the chicken.