Trim off one end of a cucumber then halve lengthwise leaving about 1/2 an inch on the opposite end to keep it intact. Rotate cucumber 90 degrees and halve lengthwise again, still keeping the opposite end intact, creating a sort of pocket.
Repeat cuts with all cucumbers then place in medium sized bowl.
Generously sprinkle cucumbers with kosher sea salt, mixing cucumbers around to coat all sides. Set aside to draw out excess moisture for about 15 minutes.
In another medium sized bowl combine green onions, carrots, onions, kochugaru, sugar, fish sauce, minced garlic, and a splash of rice vinegar and toss together thoroughly.
Rinse cucumbers under cold water to wash off salt and drain, then pat dry.
Using hands (gloves recommended) hold one cucumber from the uncut end. Using other hand scoop up a handful of filling and carefully stuff the cucumber through the opening.
Place cucumber in airtight container and repeat with remaining cucumbers. Pour any leftover filling and juice over the cucumbers in the container.
Cover and place in refrigerator for 30 minutes or eat right away. Can be kept in fridge for up to one week.