Pull 3 outer leaves off the head of cabbage and set aside. Shred the remaining cabbage in a food processor, mandolin or chop with a knife. Add it to a big bowl.
Sprinkle the cabbage with sea salt. Mix and massage the sea salt into the cabbage for about 5 minutes.
Set the cabbage aside and let it sit for 15-20 minutes so the sea salt has time to draw out the liquid and make the cabbage soft.
Hand tear the kale into bite sized pieces and add to the cabbage mixture.
Grate the radishes and carrots using a cheese grater or food processor and add to the cabbage mixture.
Add the chopped green onions, garlic, ginger, paprika and cayenne pepper to the cabbage mixture.
Mix and squeeze the cabbage mixture with your hands or a vegetable pounder. If liquid comes out when squeezed then it is ready for the next step.
Pack the cabbage in the mason jar tightly with either your hand or a vegetable pounder. Push it all the way down until it submerges in its own juices (this is the brine).
Repeat this until there is about 1½ inches of space from the top of the jar.
Roll up the leaves and place them in the jar to push the cabbage under the brine.
Screw on the jar loosely so gas can escape as fermentation takes place. Set on the counter for 5-7 days in a cool, shaded place. Place a plate under the mason jar in case it bubbles over and makes a mess.
During fermentation the sauerkraut will bubble a little and become cloudy. If scum appears, remove it with a spoon.
Remove the rolled up cabbage leaves and toss in the garbage before eating.