Heat a little oil in a large saucepan. Cook bacon over a medium high heat until well browned. A few minutes.
While the bacon is cooking, finely slice cabbage into ribbons about 1/2cm (1/4in) thick. No need to be super precise.
When the bacon is browned and starting to go crispy, remove it from the pan and drain on some paper towel. Add cabbage to the pan with 1/3 cup water. Cover and cook on medium high until the cabbage is soft or ‘al dente’ – about 10 minutes. Stir a few times during the cooking process.
Meanwhile whisk eggs and parmesan in a small bowl. When the cabbage is cooked and the water has evaporated, reduce heat to medium low. Add eggs and cook for 30 seconds on medium low heat until almost set.
Taste and season if needed, remembering the bacon is going to add more salt. Serve eggy cheesey cabbage topped with crispy bacon.