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1
Wrap the minced beef in a clean cloth and press firmly, expelling as much water as possible, so the mixture binds cleanly rather than weeping into the egg coat during cooking. Transfer to a bowl, add the crumbled tofu, ganjang, sesame oil, garlic, green onion, and diced shiitake, then mix until the seasoning is fully incorporated and the mass is cohesive. The mixture should hold its shape when pressed; if it still feels wet, press it again before moving on.
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2
Divide the mixture into equal portions and shape each into a flat round patty no more than 1.5 cm thick and approximately 5–6 cm in diameter, keeping them uniform so every patty finishes cooking at the same moment in the pan. Press the edges smooth so there are no cracks, which would cause the egg coat to split and peel away during frying. Set the patties on a tray and do not batch them in advance of the pan — they are dipped to order.
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3
Set a wide flat pan over medium heat and add enough neutral oil to coat the base in a thin, even film, so the egg coat slides rather than grips and tears when you lift the patty. The oil is ready when a drop of egg sets within two seconds without spitting — not smoking, not pooling cold. Too hot and the egg blisters and browns before the meat is through; too cool and it soaks oil rather than sealing.
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4
This is where the dish lives or dies. Take one patty, dip it immediately in the lightly whisked egg so all surfaces are coated, and lay it at once in the pan — pre-battering lets the egg begin to slacken and the coat turns uneven and thick. Repeat without crowding, which would trap steam and mottle the surface. Cook until the underside egg is set to a smooth, pale gold — not freckled, not browned, not omelette-dark — and the heat must remain at medium throughout so the egg seal looks clean and yellow rather than scorched.
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5
Turn each patty once, using a wide spatula so the delicate egg coat does not tear at the edge. Cook the second side until the egg is equally pale and set and the centre of the patty feels firm — not springy, not hard — when pressed lightly with a fingertip, which tells you the beef is cooked through without being dry. At 1–1.5 cm thickness both egg surfaces should reach pale gold at roughly the same moment the centre is done.
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6
Remove the patties to a wire rack or paper briefly so residual oil drains away rather than softening the egg crust underneath. Arrange on the serving plate in a symmetrical pattern consistent with the other jeon varieties present. Serve with cho-ganjang — ganjang and rice vinegar combined — on the side.