First, quarter the head of cabbage and then chop it to a fine texture with a knife. Place the finely chopped cabbage in a colander inside another bowl to catch the water that will drain off. Toss with a tablespoon of salt, and then set aside in the refrigerator to drain for 30 to 45 minutes.
Mix in carrot, sugar, vinegar, mayonnaise, black pepper, and cayenne. Taste and balance the flavor by adding ether salt, vinegar, or mayonnaise a little at a time.
Refrigerate until ready to serve.