Halve the cabbage, and cut out and discard the core. Slice the cabbage into 1½-inch strips. Place the cabbage in a large bowl (the bowl of a large salad spinner is ideal for this), and sprinkle with salt. Using your hands, massage the salt into the cabbage for a minute or two, until you feel it starting to soften. You'll see it start to lose volume as the salt draws moisture from the cabbage. Add cold water to cover. Place a plate, topped with a saucepan, over the cabbage to weight it down. Let all that stand 2 hours.
Meanwhile, combine the red pepper flakes, water, sugar, a pinch of salt, garlic and ginger in a food processer. Pulse until you have a rough puree. (Note: Use more or less of the chile flakes, depending on how you like your kimchi—it can range from mild to fiery. That's the beauty of making your own!) Scrape the chile paste into a small bowl, and set it aside.
Peel and julienne the radish. (A julienne peeler is helpful for this.) Cut the green onions into 1-inch pieces, including both the white and green parts.
After the cabbage is done soaking, drain, and rinse it thoroughly. Spin it dry in a salad spinner several times to dry the cabbage as much as possible.
Wipe the bowl dry, and use your hands to combine the cabbage, radish, green onions and chile paste. (Wear gloves if your skin is sensitive to chile.) Transfer the mixture to a clean 1-quart jar, packing it tightly, and leaving at least 1 inch of space at the top. Cover tightly, and let it stand at room temperature for 3-5 days. (The longer it ferments, the more the flavors develop.) Open your kimchi once a day to release any gas that forms (it's fermenting, after all), and press the mixture down with a clean spoon. After that, you can refrigerate it for up to 1 month.