Whisk one egg in a shallow dish to create an egg wash. Sprinkle half of the everything bagel seasoning onto a flat work surface.
Dip the sheets of rice paper into the egg wash, ensuring they are fully coated, and lay them flat directly over the scattered seasoning.
Spread Dijon mustard in the center of the rice paper, then layer with the slice of cheese and slices of ham.
Fold the four edges of the rice paper inward to form a square packet, leaving a small opening exposed in the center.
Transfer the assembled wrap to a baking sheet. Crack the remaining egg into the center opening and sprinkle the top with the remaining everything bagel seasoning.
Bake in the oven until the rice paper is golden and crispy, and the egg is cooked to your preference.
Cook it hands-free.
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