Place the 2 slices of ham onto a work surface, top with 1 piece of Swiss cheese, and roll up into a tight bundle. Repeat with the remaining ham and cheese.
Cut a pocket into the side of each chicken breast, taking care not to cut all the way through. (See the recipe video below for guidance.)
Smear 1 teaspoon of mustard inside each breast. Then stuff each chicken pocket with the ham bundle. Fold the breast to close the pocket, and seal it with 2 - 3 toothpicks.
Sprinkle each side of the chicken with salt, pepper, garlic powder, and paprika. Place the chicken onto a baking sheet, drizzle with oil, and bake for 25 minutes.
When the chicken is almost done, make the sauce. Place the cream, Dijon, lemon juice, and Parmesan in a microwave-proof bowl. Mix until smooth. Microwave for two 30-second intervals on high, stirring between, until warmed through and smooth. Season with salt and pepper to taste.
Remove the chicken from the oven and serve warm with sauce poured over the top.
Video
Notes
I use 4 thin slices of ham that are about 5-inches wide. I use 2 per breast because they are so thin. Just use as much as you can stuff into the chicken!
As with ham, use as much cheese as can fit into a bundle that will fit inside the chicken breast pocket. I use Swiss Cheese because I like how it melts yet still holds its form, rather than melting out of the chicken when it bakes.