Cook the cabbage: Add the shredded cabbage to the hot skillet in an even layer. Sprinkle with salt and pepper, if using. Let it cook without stirring for 2 to 3 minutes to develop some color, then stir and spread it back out. Continue to cook, stirring every couple of minutes, until the cabbage is tender with lots of golden brown and slightly charred edges, about 8 to 10 minutes total.
Beat the eggs: While the cabbage finishes cooking, crack the eggs into a bowl. Beat them with a fork until the yolks and whites are fully combined and slightly frothy.
Make space for the eggs: Once the cabbage is nicely browned and glossy, spread it into an even layer and push it slightly toward the edges of the pan, leaving a little open space in the center. If the pan looks dry, add a tiny bit more fat so the eggs don’t stick.
Add and scramble the eggs: Pour the beaten eggs over the center of the skillet, letting them run around and under some of the cabbage. Let the eggs sit undisturbed for 20 to 30 seconds, just until the edges start to set. Then gently stir and fold, pulling the cooked egg from the edges into the center and mixing it through the cabbage.
Finish cooking: Continue to cook, stirring occasionally, until the eggs form soft, golden brown curds and are just set but still moist and glossy, 2 to 3 minutes more. Avoid overcooking so the eggs stay tender and the cabbage keeps its crisp bits.
Taste and serve: Taste and adjust seasoning with a pinch more salt or pepper if needed. Spoon the cabbage and egg mixture onto plates, making sure to get those crispy, charred edges on top. Serve hot and enjoy while it’s still warm and comforting.
