Slice the cabbage: Using a sharp knife and a large cutting board cut the cabbage in half. Do the same for each half to make quarters. Cut the hard part in the bottom of the cabbage. Cut the cabbage into 1-2 inches long.
Salt the cabbage: Transfer the cabbage to a large bowl. Be sure that the bowl is extra large to have room for mixing. Add the salt and massage the cabbage with your clean hands. Pour enough water to submerge all the cabbage slices. Mix the cabbage every 30 minutes. Do this for 2-4 hours. The more salt you put, the faster for the cabbage to wilt. Check the cabbage if it is ready by grabbing a white part of the leaves. If it is not hard to bend and it is wilted, then it's ready. It's okay to have a bit of resistance. Rinse thoroughly 3 times to remove all the salt. Drain well all the excess water.
Prepare the kimchi paste: Make the rice flour paste by dissolving the rice flour and ½ cup of water in a small saucepan. Stir frequently and cook it on medium heat until the liquid becomes thick. Remove from the heat and let it cool.
In a food processor or blender, combine the peeled and sliced apple, ginger, garlic, and onion. Pulse and blend until smooth. Add the prepared rice flour paste, salted fermented shrimp, and Korean red pepper flakes (gochugaru). Blend everything until smooth and consistent just like a paste. Taste the kimchi paste and check if you need to adjust. If the paste is too salty, you can add brown sugar or more apples to balance the saltiness.
Combine all the ingredients: Peel and cut the carrots into matchstick size and cut the green onion into 2 inches long. In a large mixing bowl, combine the red kimchi paste, carrots, and green onions. Be sure to coat the vegetables well with the paste. Then add the prepared napa cabbage into the bowl. Using your clean hands or gloves, mix everything well. Make sure that the napa cabbage is well coated with the paste.
Transfer the napa cabbage kimchi to a clean mason glass jar or fermentation container. Pack the kimchi mixture tightly into the containers, pressing out any air pockets. Leave about 1 inch of space on the top. Cover with a lid.
Let your kimchi ferment to room temperature for 2-5 days. After a few days, check and taste if it's ripe and fermented already. You can leave it longer on the countertop if you want a more tangy and sour kimchi.