Remove and discard the bottom inch of the stems. Using a paring knife, peel the tough skin from the stems, and then course grate them on a vegetable grater. Place the grated broccoli stems in a bowl with a little grated fresh carrot (and a little onion, if you like). Fold in just enough good-quality mayonnaise to coat the vegetables, and season the slaw with vinegar, sugar, salt, and pepper. Cover the bowl and refrigerate the slaw for 30 minutes (this will allow flavors to marry). If the slaw becomes too runny, drain some of the juice just before serving.