How to Make It
Preheat the oven to 400°. In a medium bowl, toss the panko with the melted butter, 1 teaspoon of salt and 1/4 teaspoon of pepper. Spread on a rimmed baking sheet and bake for about 7 minutes, until lightly golden brown. Let cool slightly. Leave the oven on.
Using a small knife, cut a 5-by-2-inch pocket in the side of each chicken breast; do not cut all the way through. Place the chicken breasts between 2 pieces of plastic wrap and pound them 1/2 inch thick. Season with salt and pepper. Stuff each pocket with 2 slices of prosciutto, 1/4 cup of cheese and 1/4 teaspoon of thyme. Wrap the stuffed chicken breasts tightly in plastic wrap and refrigerate for 20 minutes.
Put the flour, eggs and toasted panko in 3 separate shallow bowls. Season the flour with 1/2 teaspoon each of salt and pepper. Whisk the mustard and a pinch each of salt and pepper into the eggs. Lightly flour the stuffed chicken breasts, tapping off the excess, then dip them in the eggs and coat with the panko, pressing to help the crumbs adhere.
In a large nonstick skillet, heat the 3 tablespoons of olive oil. Add the chicken and cook over moderately high heat until lightly browned on both sides, 8 to 10 minutes. Transfer to a lightly oiled baking sheet and bake for 15 minutes, until the chicken is golden brown outside and white throughout. Transfer the chicken to a platter, cover with foil and let rest for 5 minutes. Garnish with chopped parsley and serve with lemon wedges.