Add the gf flour to a flat bowl. Whisk the eggs in another bowl. In a third bowl, combine the breadcrumbs, almond meal, cornmeal, salt, garlic powder, and pepper.
Pound the chicken to ⅜-½” thick pieces. Sprinkle lightly with Kosher salt and pepper. Lay the prosciutto pieces down on the chicken. Add the mozzarella spices to the center of the chicken on top of the prosciutto. Add the sharp cheddar and Gruyere.
Get the skewers ready. Cut them to about 6” lengths. Spray each with a little oil to keep from sticking.
Starting at one end, roll the chicken, folding the edges in as you go. Set in place with a few skewers, “sewing” in and out along the edge and the ends. Coat in flour, then dip in egg, followed by breadcrumb mixture. Repeat with remaining chicken pieces.
At this point you can proceed to cook them or set on a clean, dry plate. Cover with cellophane and refrigerate.
Prior to cooking, bring to room temperature for 45 minutes. Preheat the oven to 400 degrees F.
Heat a skillet with 1/4" of canola or avocado oil. Brown each chicken roll in the hot oil over medium or medium low heat for 2-3 minutes on each side. Move the pieces to a baking sheet.
Bake for 10 minutes. Turn each piece over and bake for another 10-13 minutes or until a meat thermometer registers 165 in several places.
*If any of the chicken pieces are very large, you can cut them in half after pounding thinner.