Preheat the oven to 425°F. Line a rimmed baking sheet with foil, fit it with a wire rack, and spray the rack with oil.
In a small bowl, mix the mayonnaise and Dijon mustard. Season the chicken breasts on both sides with salt and pepper. Brush them on all sides with the Dijon mixture.
Dredge the chicken pieces in the almond meal, place them on the prepared wire rack, and spray their tops with oil.
Bake the chicken uncovered until an instant-read thermometer inserted into the thickest part reads 165°F, 20-30 minutes (start checking after 20 minutes). The length of time you need to bake will depend on your oven and the size of the chicken pieces.
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 the chicken to rest for 5 minutes before serving to allow the juices to redistribute and settle.
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Notes
The sodium content will depend on the brand of ham you use.
It's best to use small chicken breasts. If yours are large (8 ounces or bigger), you'll need to bake them for longer during the first baking stage, before you top them with ham and cheese. If so, keep an eye on them. You might need to loosely cover them with foil to prevent the tops from burning. Check their internal temperature with an instant-read thermometer to ensure it has reached 165°F.
You can keep the leftovers in an airtight container in the fridge for 3-4 days. You can reheat them covered in the microwave. However, I don't like reheated chicken, so I eat the leftovers cold with quick pickles on the side.