Chop the carrot ends off and discard, then chop the carrot into 1 inch chunks and put in the food processor. Process until minced.
Cut the cabbage in half, then cut out the core. Slice each quarter into one inch slices. Place one sliced quarter into the food processor and pulse until finely chopped. Be careful not to overprocess or it will become puree. When it's just right, remove the finely chopped cabbage and carrot into the large bowl.
Repeat the chopping process with the other three quarters of the cabbage, one quarter at a time, adding all the finely chopped cabbage to the big bowl.
Slice the green onion and add to the bowl of cabbage.
Add the mayonnaise, mustard, pickled jalepenos, paprika, garlic, apple cider vinegar, onion powder, sugar, celery seed, and cayenne pepper to the food processor. Blend until smooth.
Pour the dressing over the cabbage mixture and stir to combine.
Taste and add hot sauce, salt, and pepper if desired.