Trim off the very bottom 1/2'' of the stalks of broccoli. Roughly chop. Transfer to a food processor in batches, if needed, and pulse until just finely chopped. Don't over-process the broccoli! Pour the minced broccoli into a large bowl.
Using a microplane, zest the lime straight into the bowl of broccoli.
Prepare the dressing:
Juice the lime into the food processor. Add the jalapeño, cilantro, vegan mayonnaise, and hot sauce. Blend until completely combined and smooth.
Finish the slaw:
Pour the dressing over the broccoli and toss to combine. Add the finely minced red onion and season to taste with salt and pepper. Transfer to a serving bowl and refrigerate until needed.
To serve:
Before serving, garnish with more minced cilantro and a few slices of jalapeño if you like. Enjoy!