Prep the Cucumbers. Wash and trim the cucumbers. Slice them lengthwise into quarters, leaving one end attached so they form a cross. Sprinkle with salt, then let them sit for 30 minutes. Rinse and drain.
Make the Kimchi Paste. In a bowl, mix gochugaru, garlic, ginger, sugar, green onions, and carrots (if using). Stir in a splash of vinegar for brightness if desired.
Stuff the Cucumbers. Carefully stuff each salted cucumber with the spicy filling, making sure the mixture gets between all sections.
Pack & Rest. Place the stuffed cucumbers in an airtight container. Let them sit at room temperature for 4–6 hours to ferment slightly, then refrigerate.
Enjoy. Your cucumber kimchi is ready to enjoy once chilled, and it gets even better after a day or two in the fridge.