Thoroughly wash the cucumber, radish, and carrot. Slice them thinly or cut them into strips, according to your preference for pickles.
In a small saucepan, combine the rice vinegar, water, sugar, and salt. Heat over medium heat until the sugar is completely dissolved, stirring occasionally.
Thinly slice the garlic and ginger. Add them, along with the gochugaru, to the hot vinegar mixture. Allow to cool completely.
In a clean, sealable jar, layer the vegetables. Pour the cooled spicy vinegar brine over the vegetables.
Press down on the vegetables with a spoon to ensure they are completely submerged in the liquid. Seal the jar.
Refrigerate for at least 24 hours to allow the flavors to meld and develop.
Before serving, sprinkle with toasted sesame seeds. Serve as a side dish with sushi, rice dishes, or grilled meats.
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