Chicken stuffed with ham and cheese, breaded, fried, cream sauce poured over top. Cordon bleu is the high calorie chicken dinner that never stopped being impressive.
Butterfly each chicken breast by slicing horizontally, leaving a hinge. Place between plastic wrap and pound to 1/3-inch thickness with a meat mallet.
Season chicken with 1 tsp salt and 1/2 tsp pepper. Layer 2 slices of ham and 2 slices of Swiss cheese on each breast, then tightly roll up, tucking in sides. Secure with toothpicks.
Dredge each roll in flour, then dip into beaten eggs, and coat thoroughly with panko breadcrumbs. Press gently to adhere.
In a large skillet, heat vegetable oil to 350°F (medium-high). Fry chicken rolls on all sides until deep golden and cooked through (8–10 minutes total). Transfer to a wire rack to drain; let rest 5 minutes.
For sauce: In a saucepan, melt butter over medium heat. Whisk in 2 tbsp flour and cook 1 minute. Gradually pour in milk and cream while whisking constantly. When thickened, add Parmesan, Dijon mustard, 1/2 tsp salt, and 1/2 tsp pepper. Simmer 2–3 minutes until creamy.
Slice each cordon bleu. Spoon warm cream sauce generously over the top and serve immediately.