Preheat oven to 425 degrees F. Line a baking dish with foil, fit it with a wire rack and spray the rack with oil.
In a small bowl, mix the mayonnaise and the Dijon mustard.
Season the chicken breasts on both sides with salt and pepper. Brush on all sides with the Dijon mixture. Dredge in the almond meal, and place on the prepared wire rack. Spray with oil.
Bake, uncovered, until an instant-read thermometer inserted into the thickest part reads 165 degrees F, 20-30 minutes (start checking after 20 minutes). How long you need to bake will depend on your oven and on the size of the chicken breasts.
Top each chicken breast with two slices of ham (folded in two if necessary) and a slice of Swiss cheese.
Return the chicken to the hot oven for 2-3 minutes, just until the cheese melts. Garnish with chopped parsley. Allow to rest 5 minutes before serving, to allow the juices to redistribute and settle.
*Sodium content will depend on the brand of ham you use.