To make the rice: Process the cauliflower in a food processor until it becomes a bunch of little crumbs.
In a bowl. stir in the rest of the ingredients, by hand, with the cauliflower.
Julienne all of the vegetables (in other words, cut into small strips)
For each nori sheet, spread on ¼ of the rice evenly, leaving one edge of about ½ inch (1-cm) without rice.
Sprinkle a little water on this edge when you roll up the sheet, starting from the opposite side.
This will help everything stick together.
Arrange a few slices of avocado, pepper and carrot.
Roll up tightly and cut with a sharp knife.
Serve with the peanut sauce.
Peanut Sauce:
Blend all of the ingredients together until smooth, adding more water if you need to.
Notes
My note: To make ahead - after all of the rolls are set on a plate - dot the tops with lime juice to keep the cauliflower and avocado from turning brown. Cover with plastic wrap and store in the refrigerator.