Slice the cucumbers thin, about 2-3 mm, on a mandoline if you have one or diagonally by hand.
Toss with 1 tsp salt in a colander set over a bowl and let sit 10-15 minutes, until visibly wilted and pooling water underneath.
Squeeze the slices gently in small handfuls to press out the drawn water. Taste one — it should taste seasoned, not harshly salty. Rinse briefly and squeeze again if it's too salty.
Whisk gochugaru, vinegar, sugar, and garlic together in a bowl until the sugar dissolves.
Add the squeezed cucumber and scallion to the dressing only when you're ready to eat, and toss to coat.
Finish with sesame oil and sesame seeds, tossed in at the very end.