How to Make It
Prepare the Egg Rolls: Combine beef, onion, bacon, garlic, soy sauce, salt, and pepper in a bowl; form mixture into 3 (3/4-inch-thick) patties. Heat 1 tablespoon peanut oil in a large cast-iron skillet over medium-high; add patties, and cook until cooked through, about 6 minutes per side. Remove from pan, and let cool.
Break burgers into 1/2-inch chunks. Gently toss together burger pieces, lettuce, pickles, mayonnaise, and mustard in a bowl until combined. Place egg roll wrappers on a work surface with a point towards you. Combine egg and 1 tablespoon water in a small bowl. Place 1/4 cup burger mixture in the middle of 1 wrapper; top mixture with 1 cheese piece. Fold point closest to you over mixture, tucking in tightly. Brush all exposed sides of wrappers with egg mixture. Fold over sides, pressing to adhere; roll over to seal. Place on a baking sheet dusted with cornstarch. Repeat procedure with remaining burger mixture and wrappers. Cover with plastic wrap, and chill until ready to use.
Prepare the Special Sauce: Combine ketchup, mayonnaise, soy sauce, vinegar, sugar, and cayenne pepper in a bowl; cover and chill until ready to use.
Heat 8 cups peanut oil to 360°F in a large Dutch oven over high. Add egg rolls; cook, turning occasionally, until golden brown, about 2 minutes. Drain on paper towels, and sprinkle with sesame seeds. Serve with Special Sauce.