In a large pot (you'll need ALL the room!) brown the hamburger or sausage, leaving the fat. Add the chopped onions and cook until translucent. Add the cabbage and caraway, salt and pepper to taste. Cook the cabbage al dente - not to mush, but still firm enough to resist your teeth a bit when you bite.
Add caraway. It's a heavy-duty spice, so I cut it back from the original 1 tablespoon, but you can give it a taste before you use it and see if it's good for you. You can also try some red pepper flakes for a little punch.
When the dough has risen, turn it out again onto a heavily floured board or surface. You'll need to cut it into 24 somewhat even pieces. I cut the big lump in 1/4, then stretched those pieces out and cut them into 6 pieces. A little variation is fine. Cover your pieces with plastic wrap while you work rolling them out. (I find rolling it all out and cutting round circles just doesn't work as well.)
Roll a piece of dough into a ball, then with a rolling pin roll it out to about 1/8" to 1/4" thick. Even at 1/8" you'll have plenty of bread, so don't worry about making them too thin. You should have a circle about 6" in diameter.
Place 1/2 cup filling in the center, then top with 1 tbsp of cheese. Pull up opposite sides of the circle and pinch them together. Pull the OTHER sides together and do the same. Pinch up the sides to seal all the way, fold all this under the roll and place that side down onto a greased sheet or baking pan. (If you like, you can brush each roll with the egg wash - just beat one egg with a little water until it's a light yellow, then use a pastry brush to coat the top of each roll).
Bake the rolls at 350 for 25 minutes, until the rolls are golden brown.