Melt ghee in a large frying pan that has a fitted lid over medium-high heat.
Add cabbage and salt. Toss with the melted ghee.
Continue cooking over medium-high heat until the cabbage browns, about 3-4 minutes.
Mix in apple cider vinegar and pepper.
Gather cabbage into two small mounds. Using the back of a spoon, form a well in each mound to create space for the eggs.
Crack an egg into each indentation in the cabbage.
Reduce the heat to low-medium and cook until whites of egg firm and yolk reaches desired consistency. Approximately 1.5 minutes for runny yolk, 2 minutes for slightly firm yolk, 2.5 minutes for solid yolk.