Pre-heat a skillet over medium heat and pre-heat an oven to 350 degrees F.
Add the lightly beaten eggs to a large mixing bowl.
Spread 1/2 tbsp(s) of whole grain mustard aioli on each pita half. To assemble each sandwich, top 1 pita half with 1 slice of gruyere cheese, 4 slices of ham, and 1 additional slice of gruyere. Aioli side in, close the sandwich with additional pita half; Repeat for remaining sandwiches.
For each sandwich, add 1 Tbsp(s) of butter to the skillet and dip each sandwich in egg wash before griddling both sides for 5 minutes or until golden.
Transfer the skillet to the oven and allow to bake for an additional 5 minutes or until cheese is bubbly.
Cut each sandwich in half again (optional) and dust with powder sugar before serving.