Prepare the Chicken – Flatten chicken breasts to an even thickness using a meat mallet. Layer each piece with ham and shredded Gruyere cheese, then roll tightly and secure with toothpicks.
Create the Crispy Breading – Toast panko breadcrumbs in butter and olive oil until golden brown. Mix with Parmesan cheese and seasonings.
Coat the Chicken – Whisk together Dijon mustard, honey, and olive oil to create a flavorful wash. Brush each rolled chicken breast with the Dijon mixture, then coat with the toasted panko mixture, pressing to adhere.
Bake to Perfection – Place the chicken rolls on a wire rack over a baking sheet. Bake at 350°F for 30-35 minutes until golden and cooked through.
Make the Dijon Cream Sauce – Simmer chicken broth, heavy cream, Dijon mustard, and seasonings in a saucepan. Whisk in cornstarch to thicken, then simmer until creamy and smooth.
Serve and Enjoy – Slice the chicken and drizzle with the warm Dijon cream sauce. Garnish with fresh parsley and serve with your favorite sides.