Preheat air fryer to 350°. Beat 1 egg and pour into a greased 8x4-in. disposable foil tray; place in air-fryer. Cook until set, 3-4 minutes. Carefully remove egg from tray. Cut in half; fold each portion in half.
Combine butter, onion and mustard. Drizzle cut side of each roll half with 1 teaspoon butter mixture. Layer roll bottom with 1 folded egg portion, 1 slice ham, 1 slice cheese, 2 bacon strip halves, remaining folded egg portion, 2 pickles and roll top; return to foil pan. Drizzle sandwich with 1 teaspoon butter mixture. Cook until cheese is melted and roll is browned, 3-4 minutes. Repeat with remaining ingredients.
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