• Preheat your oven to 400 degrees Fahrenheit. Spray a baking dish with cooking spray and set aside.
• Slice the chicken breasts in half by butterflying them open and then cutting all the way through to cut into two cutlets. Place each cutlet on a piece of plastic wrap. Top with another piece of plastic wrap and pound the cutlets thin using a meat mallet or a rolling pin.
  1 pound boneless skinless chicken breasts
• Remove the top pieces of plastic wrap and season the cutlets with salt and pepper.
  salt and pepper
• Place a slice of ham on top of each cutlet. Top with 1/4 cup shredded cheese.
  4 slices deli ham, 1 cup Swiss cheese
• Roll up each chicken breast in the plastic wrap. Twist the sides of the plastic wrap and put them under the rolled-up chicken. Let the chicken rest while you prepare the coating. (See note.)
• Mix the salt and pepper into the flour in a shallow dish. In a separate shallow dish, mix the panko breadcrumbs with the thyme, garlic, and melted butter.
  1/4 cup all-purpose flour, 1/2 teaspoon kosher salt, 1/8 teaspoon freshly ground black pepper, 1 cup panko breadcrumbs, 2 teaspoons dried thyme, 1 garlic clove, 1 1/2 tablespoons unsalted butter
• Remove the plastic from the chicken roll-ups. Dip each rolled-up chicken cutlet into the seasoned flour.
• Dip the chicken in the eggs. Then dip the egg-coated chicken roll-ups in the panko mixture. Place seam side down in the prepared baking dish.
  2 large eggs
• Bake for 20 minutes or until the inside of the roll reaches 165 degrees Fahrenheit. Use a meat thermometer to make sure it is fully cooked.

Sauce

• While the chicken is baking, make the sauce. In a small saucepan, melt the butter over low heat. Add the garlic and sauté until fragrant, about 30 seconds. Season with ground mustard, salt, and pepper.
  1 1/2 tablespoons unsalted butter, 1 garlic clove, 3/4 teaspoon ground mustard, 1/2 teaspoon kosher salt, dash of black pepper
• Whisk in the flour. Turn the heat up to medium-low. Then slowly whisk in the wine. Add a little of the liquid, whisking until it is absorbed by the roux (the butter and flour combination). Add more liquid once what you just added is absorbed. The more liquid you add, the more quickly you can add it.
  1 1/2 tablespoons all-purpose flour, 1/3 cup white wine
• Stir in the half and half. Continue stirring as you bring the sauce to a simmer. Simmer for five minutes over medium-low heat (you should see regular bubbles), stirring regularly.
  3/4 cup half and half
• Serve with the baked chicken cordon bleu and enjoy!