Prep the onion wrap: Slice the onion into very thin, wide sheets or ribbons. Pat them dry with paper towels to remove extra moisture. Set up a dipping station with flour–cornstarch mix, whisked eggs, and breadcrumbs for a light coat.
Shape the patties: Gently form two equal patties (about 3/4-inch thick). Make a small shallow indent in the center of each to prevent puffing as they cook. Season with salt and pepper on both sides.
Heat the cooking medium: In a skillet or on a grill pan, get your surface hot. If you’re pan-searing, a light brush of oil helps prevent sticking.
Cook the beef: Sear the patties 2–3 minutes per side. When you flip, place a cheese slice on one patty and top with the other patty to trap the cheese inside. Gently press the edges to seal and let the cheese melt, about 1–2 minutes more. You’re aiming for a nicely browned exterior and a still-juicy center.
Prepare the onion wraps: Lightly dust an onion sheet in the flour–cornstarch mix, dip in egg wash, then coat with breadcrumbs. Fry in the hot oil, 1–2 minutes per side, until deeply golden and crisp. Drain on paper towels and sprinkle with a touch of salt.
Assemble the wrap: Lay a crisp onion sheet on a clean surface. Transfer the hot, cheese-stuffed patties onto the wrap so the cheese stays melty. Gently wrap the onion sheet around the burger, securing with a toothpick if needed. The wrap should hug the patty and give a satisfying crunch when you bite in.
Finish and rest: Let the wrapped burger rest for a minute to meld the flavors and soften the crisp shell just enough to bite through. Then slice if you like, or serve whole for a dramatic presentation.
Serve with a quick dip: Pair with a simple mayo–ketchup sauce or your favorite burger condiment to brighten the rich beef and onion notes.