Prepare Wood Ear Mushrooms: Soak the wood ear mushrooms in cold water, squeeze, and finely julienne them.
Prepare Cucumber: Scrub the cucumber with coarse salt, cut it into 4 pieces, peel, and julienne.
Prepare Shiitake Mushrooms: Remove the stems from shiitake mushrooms, slice, and finely julienne.
Prepare Other Vegetables: Julienne the burdock root, zucchini, and carrot.
Blanch Mung Bean Sprouts: In a heated pan, blanch mung bean sprouts with a cup of water.
Make Soy Sauce Seasoning: Mix soy sauce, cooking wine, sugar, minced garlic, sesame oil, and pepper.
Stir-Fry Vegetables: In a heated pan, stir-fry shiitake mushrooms, cucumber, zucchini, and carrot in order, adding a pinch of salt to each.
Braise Burdock Root: Transfer vegetables to a plate, add julienned burdock root and half of the soy sauce seasoning to the pan with remaining water, and braise.
Make Miljeonbyeong Batter: Mix flour, water, salt, and sesame oil in a bowl.
Cook Miljeonbyeong: Over low heat, add oil to a pan, wipe off excess, and spread a spoonful of batter into a thin circle.
Assemble Guseolpan: Arrange the fillings around the center of a plate and stack the miljeonbyeong in the center.