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Gwangjang market is famous for its thick mung bean pancake (bindaetteok) which tastes different from other places. The ajummas here can speak Chinese very well and they will tout from their stalls. Some stalls have their mungbeans freshly grounded on the spot.
I would recommend to scan the whole area and see which one looks the best to you before settling down on one. Some stalls sell thinner ones, so just keep a lookout. We had this from Stall 59, and it was one of the thickest one around. It was crispy on the outside and just the right texture on the inside. But it wasn't really tasty.
Other food items I recommend to have would be: 마약김밥 (different stalls different prices), ssikhye (W1,000 per cup). They have sundae, tteokbokki, twigim, and fried fish, and octopus. Feel free to explore everything before settling down on one! Or you can pick a bit from here and there.