Add the sliced cabbage to the skillet. Toss it with the onions and butter, using tongs or a large spoon to coat the cabbage. Cook, stirring every couple of minutes, until the cabbage is tender and lightly browned in spots, about 8 to 10 minutes.
While the cabbage cooks, open the cans of clams and drain them well. If you like a bit more moisture in the finished dish, reserve about 1/4 cup of the clam juice and set it aside.
When the cabbage is tender and most of its moisture has cooked off, sprinkle in a small pinch of salt and a few grinds of black pepper. Go easy on the salt at first, since the clams and cheese will add more seasoning.
Toss the drained canned clams into the skillet, spreading them out evenly over the cabbage and onions. If using, pour in the reserved 1/4 cup clam juice to keep everything moist and saucy.
Stir gently to combine the clams with the cabbage and onions, then cook for 2 to 3 minutes, just until the clams are heated through. Avoid overcooking so they stay tender.
Reduce the heat to low. Sprinkle the shredded mozzarella cheese evenly over the top of the clam and cabbage mixture.
Cover the skillet with a lid or a sheet of foil and let it sit over low heat for 2 to 4 minutes, just until the cheese is melted and gooey.
Remove the lid, taste, and adjust seasoning with a bit more salt and pepper if needed.
Serve the clam skillet hot, right from the cast iron pan, making sure each portion gets plenty of cabbage, clams, and melty cheese.
