Wash the cabbage and peel carrots. Remove a large outer leaf and set aside. Cut the cabbage in half and then in quarters, remove the core and tough outer ribs with a sharp knife, then slice the cabbage in approximately ¼" thin slices and grate the carrots.
In a large mixing bowl combine the cabbage, carrots, salt and sugar, then start mixing ingredients with your hands while massaging them to soften the cabbage and allow it to release its juices for 2-3 minutes.
Pack the cabbage and carrots tightly in a sterelised jar, use a long-handled wooden spoon to pack your cabbage and to release more juice. When your jar is full the liquid should cover the cabbage completely, which will preserve it from harmful bacteria. Cover the surface with a reserved cabbage leaf and weigh it down with a water-filled jar, then cover with a layer of cheesecloth. Leave your sauerkraut out to ferment for approximately 3 days. It might take longer if your house is cold. Each day pierce it with the handle of a wooden spoon to release gas, then cover it back up with a cheesecloth.
Refrigerate the sauerkraut after the fermentation process is done.