Coarsely grate the carrot and finely shred the cabbage (use a food processor with a grating/ slicing blade or do it by hand) and tip into a bowl. Season with salt, then add the sugar and vinegar and toss everything together. Leave for 20 mins for the vegetables to very lightly pickle.
Stir through the mustard and mayonnaise and add any other bits you want to, then serve. Can be made a day ahead and chilled.