Wash the cabbage leaves in cold water. Bring a pot of water to a boil, add salt, and put in the cabbage leaves. Cook at a moderate boil until tender, then drain. As soon as they are cool, chop them fine.
Turn on the broiler.
Put the oil and the garlic in the skillet, turn on the heat to medium, and cook the garlic, stirring frequently, until it becomes colored a pale gold.
Add the chopped cabbage, turn it over several times to coat it well, cook for 2 or 3 minutes, then turn off the heat.
Break the eggs into a bowl, beat them with a fork until the whites are indistinguishable from the yolks, then transfer the cabbage to the bowl. Add liberal grindings of black pepper. (Do not clean the skillet.) Turn the contents of the bowl over several times to combine the cabbage and beaten eggs into a well-integrated mixture.
Empty the bowl into the skillet, and cook, uncovered, at very low heat. When the eggs have set and thickened, and they are creamy only in the center of the pan, run the skillet briefly under the broiler, proceeding as described in the directions for Basil Frittata.