Wash the radish & greens thoroughly and cut the radish into bite sized, uniform pieces.
In a large glass jar, put the greens on the bottom then add the radishes on top. Sprinkle with 2 tbsp Korean sea salt and shake until everything is evenly coated with salt. Let it sit on the counter for 1 hour.
Cut a Korean melon in half lengthwise and remove the seeds. Cut into thin pieces and remove the skin if you prefer (I leave it on). Cut 1/4 of an Asian pear and cut into thin pieces as well. Poke holes into the chili peppers with a fork. Put the garlic, ginger, and onion in to a cheesecloth or tea bag. Cut the green onions in to 3 inch long pieces.
Soak the dried kelp in 10 cups of cold water for 30 minutes.
Set the kelp aside (you can use this to make something else), then add plum syrup and 3 tbsp Korean sea salt and mix until dissolved.
After 1 hour, the radish and greens should be softened and there will be a pool of water at the bottom. Leave it- that's where a lot of the flavor is coming from.
Add the chili pepper, melon, pear, ginger, garlic, onions, green onions, and water mixture.
Secure the lid and let this ferment on the kitchen counter for 1-2 days, depending on how sour you like it.
After 1 day the water will turn a little darker, less translucent, and there will be bubbles floating to the top. This means it is fermenting! taste to see if it is to your liking- when it's good for you, store in the fridge for up to 2 months.
Slice the chili peppers to serve and add a few ice cubes to keep it extra cold. Try the melon! It is not a common ingredient in Dongchimi but I had some like this in Busan where my family is from, and it is really delicious.