Bring a large pot of lightly salted water to a boil. Slice off the bottom of the cabbage and plunge into the boiling water. After a few minutes remove the head, run under cold water and peel off leaves; they should be soft enough to flatten but not soggy. Drain well.
Cook the ground beef with the water in a sauce pan, breaking up larger pieces with a fork, until meat is no longer pink. Drain well.
Lightly spray a 9-by-13 inch baking pan with vegetable oil. Heat the oven to 350 degrees. In a blender or food processor, pulse the ricotta with the egg and parsley.
Cover the bottom of the baking pan with about 1 1/2 cups marinara sauce. Add a layer of cabbage leaves, making sure to overlap. In layers, add half the ground beef, half the ricotta mixture and more cabbage leaves. Spoon on about 1 cup of sauce, then half of the mozzarella.
Add another layer of cabbage, the remaining beef, the remaining ricotta, any remaining cabbage leaves and the remaining sauce. Top with remaining mozzarella and the Parmesan.
Bake about 1 hour, until lasagna does not appear watery and cheese is melted and browned as desired. (Cover pan loosely with foil if cheese browns too quickly.)
You may substitute alfredo sauce for the marinara, omit the meat or add layers of prosciutto, sliced zucchini, carrots, and/or mushrooms. Instead of cooking the cabbage, you may place the whole head in the freezer for 24 hours, then defrost for 30 minutes; the softened leaves will pull off easily.