Bring a large pot of water to boil.
Sprinkle sliced cucumbers with salt, gently toss, then set aside to draw water out of the cucumbers while you prepare the remaining vegetables.
Ladle ¼ cup of the boiling water from the pot over the julienned radish in a small bowl or glass jar. Add 2 tablespoons rice vinegar and 1 teaspoon salt. Stir to dissolve salt, and let radish "pickle" while you prep the rest of the ingredients.
Drop bean sprouts into boiling water. Return water to a boil, then turn down to a simmer. Blanch the sprouts until they are just beginning to wilt, about 10 minutes. Remove the sprouts from the pot with tongs, large slotted spoon, or small colander. Drain off or squeeze as much water from the sprouts as possible. Toss with ½ teaspoon salt, 1 teaspoon sesame oil, and 1 teaspoon crushed toasted sesame seeds (optional). Set aside.
Drop zucchini into the same boiling water and blanch to just before they begin to wilt, about 5 minutes. Remove zucchini from the pot with large slotted spoon or small colander. Gently shake the zucchini to drain off as much water from the zucchini as possible, and set aside in a small bowl. Toss with ½ teaspoon salt and 1 teaspoon sesame oil.
Continue the same method of drop-blanch-remove-drain for the julienned carrots. Carrots will take about 10 minutes to soften. Toss with ½ teaspoon salt and 1 teaspoon sesame oil.
Repeat process for spinach, which will blanch in about 3 minutes. Toss with Toss with ½ teaspoon salt and 1 teaspoon sesame oil.
Rinse cucumbers to remove salt and liquid. Squeeze out excess liquid. Toss with ½ teaspoon sesame oil and ¼ teaspoon gochugaru, Korean chile powder, if using.