Place the cabbage on a cutting board.
Using a small pointed knife, cut around the core in the shape of a cone. Keep going until the core is loose. Pull it out and discard.
Drop the cabbage into the boiling water, cored side down, and let the water come to a rolling boil once more.
Lower the heat, cover the pan and cook the cabbage for about 10 minutes.
Scoop out the cabbage and dump in a bowl of iced water. When cool, place in a strainer, cored side up, and allow to drip for a few minutes.
Carefully loosen the cabbage leaves to separate.
Take one cabbage leaf and, using a sharp knife, shave off the thick portion that runs vertically in the middle of the leaf. Be careful not to shave too deep to avoid tearing the cabbage. Do this with all the cabbage leaves.
The too small ones near the core, you may chop finely and mix into the filling. But that's entirely optional.