Put the cabbage, onion, parsley. and seasonings in a large bowl. Toss to mix. Pour the beaten eggs over the mixture, and toss to coat. Sprinkle on the flour, and, again, toss to coat.
Warm the vegetable oil in a 10-inch non-stick skillet over medium-low heat. Add the cabbage mixture, and mash it down lightly with a spatula. Then run the spatula between cabbage and skillet to create a round, or "pie" shape. Cover the skillet, and let cook until richly browned on the bottom -- about 10 minutes.
Flip the pie. To do this, slide the pie, top side up, onto a large plate,. Carefully place the skillet over the pie, and then invert so that the bottom of the pie is now on the top. Cook, covered, until done -- about 7 minutes. Slide the pie onto a plate or serving platter, cut it into wedges, and enjoy!