Flip the cauliflower over so the core is facing up, then cut it in half. Remove the leaves and discard.
Remove the triangular core piece from each half, then cut the cauliflower into small florets. Place the florets into a large bowl filled with water, then drain the cauliflower florets. Lay the cut cauliflower on a large tea towel to dry.
Set up the food processor with the grating or "S" blade. Fit each piece of cauliflower into the grating tube and turn the processor on. Repeat until all the cauliflower has been grated.