Cut cabbage into 2-inch pieces and place in a large mixing bowl.
Cover cabbage with water and salt. Press down on the cabbage with a plate until water comes over the top. Let sit for 45 minutes.
Cut carrots and daikon into matchsticks (a mandoline is helpful here). Set aside.
Cut green onions into ¼-in. pieces and set aside.
In a food processor, blend the remaining ingredients to form a thick paste.
Drain and rinse cabbage, then put it back in the bowl. Add carrots, daikon and green onions.
Coat veggies well with the pepper paste, then transfer to a fermentation pot or glass jar.
If using a fermentation pot, place the ceramic weights firmly down onto the veggies. Otherwise, press a plate or piece of wood onto the veggies until liquid comes over the top. Then place 2 rocks on the wood or plate. Cover loosely with a lid.
Let kimchi ferment for 5 days to 2 weeks, tasting every few days until it reaches a sourness you like. Keep in mind it will continue to ferment a little after you put in the fridge.
Transfer finished kimchi and liquid to glass quart jars with lids. Store in the fridge.