Cucumber Kimchi (Oi Kimchi)

Steps

1. Wash the mini cucumbers, scrubbing the skin, trim the ends, then cut them into 2 1/2-inch (6 cm) sections. Stand each section on end and cut a cross down two thirds of its height, about 1 1/2 inches (4 cm), leaving 1/2 to 3/4 inch (1.5 to 2 cm) intact at the bottom so it stays in one piece.
2. Put the sections in a bowl and sprinkle with the coarse salt, gently spreading the cuts to slip a few grains inside. Toss and let them sit for 45 minutes to 1 hour, turning them halfway through. They're ready when a section bends a little under your fingers without snapping and the cuts open without splitting.
3. Meanwhile, mix the gochugaru and water in a large bowl and let it swell for 5 minutes: you'll get a vivid red paste. Grate the garlic and peeled ginger over the bowl, then add the fish sauce and sugar, and stir.
4. Cut the carrot into a fine 1 1/2-inch (4 cm) julienne, slice the onion paper-thin, and cut the green onions into 1 1/4-inch (3 cm) lengths, splitting the white parts in half if they're thick. Add everything to the paste and mix with gloved hands until the vegetables are evenly red.
5. Rinse the cucumbers quickly twice in cold water to remove the surface salt, then let them drain in a colander, cut side down, for 10 minutes. Pat them dry with a clean kitchen towel.
6. Gently open each section and tuck a small pinch of filling into the cuts with your fingertips, without forcing it so the cucumber doesn't split. Then roll the section in the paste left in the bottom of the bowl to coat the outside.
7. Pack the sections tightly, standing up, in a jar or airtight container of about 1 1/2 quarts (1.5 l). Spread the rest of the filling on top, pour in the juices left in the bowl, and press down lightly. Close the lid.
8. To eat it right away, serve it chilled: it's crunchy, spicy, and bright. For a fermented flavor, leave the jar at room temperature, between 64 and 72°F (18 and 22°C), for 1 to 2 days, until you see small bubbles and smell a slight tang, then refrigerate.
9. When serving, take out a few sections with clean chopsticks, arrange them in a small dish with some of the filling, and sprinkle with sesame seeds.