1Heat the oven to 400°F. Set a wire rack on a baking sheet and spray or brush the rack lightly with oil so the chicken won't stick.
2Slice each chicken breast horizontally almost all the way through and open it like a book. Cover with plastic wrap and pound to about 1/4 inch thick. Season both sides with salt and pepper.
3Brush the inside of each breast with 1/2 tbsp Dijon (2 tbsp total). Lay a slice of ham and a slice of swiss on top, folding them to fit inside the edges of the chicken.
4Roll each breast up snugly, tucking in the sides as you go, and secure the seam with toothpicks if needed.
5Set up three shallow dishes: flour mixed with the paprika, garlic powder, and a pinch of salt in the first; beaten eggs in the second; panko tossed with parmesan and the 3 tbsp melted butter in the third.
6Dredge each roll in the seasoned flour and shake off the excess. Dip in the egg, then press firmly into the buttered panko until fully coated.
7Set the rolls seam-side down on the rack. Bake 30 to 35 minutes, until the crust is deep golden and the chicken reads 165°F in the center.
8While the chicken rests, melt the remaining 1 tbsp butter in a skillet over medium heat. Cook the shallot 2 minutes until soft.
9Pour in the broth and simmer until reduced by about half, 3 to 4 minutes. Stir in the cream and remaining 1 tbsp Dijon and simmer 2 to 3 minutes until lightly thickened. Season with salt and pepper.
10Remove the toothpicks, slice the rolls on a bias if you like, and spoon the sauce over or alongside. Finish with parsley.