Preheat a conventional oven to 390°F (200°C), or a fan oven to 350°F (180°C).
Spread the panko on the rimmed baking sheet and lightly coat it with oil spray. Bake for about 3 minutes, until light golden, then immediately transfer it to a bowl.
Cut a deep pocket into the side of each chicken breast without cutting through the opposite edge.
Fold two Swiss cheese slices for each breast. Arrange the ham around the cheese, place the bundles inside the pockets, and secure each opening with approximately two toothpicks. Season the chicken with salt and black pepper.
Mix the mayonnaise with 1½ Tbsp Dijon mustard. Spread it over the tops and sides of the chicken, leaving the undersides uncoated.
Press the toasted panko onto the coated surfaces and mist lightly with oil spray.
Bake for 25–30 minutes, until the crumbs are golden and crisp and both the thickest chicken portion and filled center reach 165°F (74°C).
Meanwhile, melt the butter in a small saucepan over medium heat. Add the flour and cook for 1 minute.
Whisk in half the milk until smooth. Add the remaining milk, 2 Tbsp Dijon mustard, and Parmesan. Whisk for about 3 minutes, until thickened but pourable. Season with salt and black pepper.
Remove every toothpick and serve each chicken breast with approximately ½ cup warm Dijon cream sauce.