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1
Cut each cucumber into lengths of approximately 6 cm. Stand each piece upright and cut an X down through the centre, stopping 1–1.5 cm from the base — the four quadrants must remain joined at the foot — so the pocket holds the filling without the piece falling apart during stuffing or serving. Check by gently pressing: the pocket opens but the base holds firm.
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2
Rub the coarse sea salt firmly into the cut surfaces of each cucumber piece, working it deep into the scored pocket so the salt draws moisture from the centre of the flesh, not just the outer skin. Set the pieces upright in a colander and leave for 20–30 minutes only — no longer — because beyond that point the cucumber loses the rigid core that gives the finished dish its crunch. It should feel slightly softened on the outside but still firm when pressed between finger and thumb.
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3
Meanwhile, julienne the radish and place it in a bowl; if it has released water, squeeze it firmly in a clean cloth until the filling mass feels dry to the touch, so it does not dilute the seasoning or turn the pocket soggy. Add the buchu, gochugaru, garlic, ginger, saeujeot, and sesame seeds and toss briefly to combine. The filling should cohere without visible pooled liquid.
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4
Rinse the salted cucumbers briefly under cold water and pat dry. Open each pocket and pack the filling in immediately, under slight, even pressure until it sits flush with the top — do not pre-score and leave the cucumbers to stand, as the cut surfaces will begin to weep and the filling will slide rather than hold. The four quadrants should splay just enough to show the red filling at the centre without splitting apart.
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5
Arrange the stuffed pieces upright or on their sides in a single layer in a covered container and store refrigerated, so the pieces keep their shape rather than compressing one another. The dish is ready to eat immediately and reaches its best texture within a few hours as the filling scents the cucumber flesh. It must be consumed within 3–5 days; beyond that point the crunch — which is the whole purpose of the dish — is lost.