Add each cabbage separately to a food processor or blender and process the cabbage until it is in small enough bites. You can also chop the cabbage and other ingredients by hand with a knife. Add each batch of chopped cabbage to a large mixing bowl.
Peel and cut up the apple, and add it to the processor. Also add the remaining ingredients to be chopped together with the apple. Process and then add this batch to the mixing bowl.
Add the remaining ingredients (the dressing) in separate bowl to taste, or you can do what I do a lot of the time - add them to the main mixing bowl with the chopped salad, and adjust until you have the desired taste.
Place the coleslaw in the refrigerator until you're ready to serve and eat it!