1. Cut the cabbage into thin slices and cook it in water (in 2 different waters).
2. Cook the potatoes.
3. Finely chop the onion and garlic, and sauté them in butter.
4. Cut the bacon slices into thin strips and fry them with the onion and garlic.
5. In a gratin dish, place 4 small pieces of butter, then add the cooked cabbage and potatoes.
6. Add the bacon with its juices.
7. In a bowl, beat half of the eggs with a tablespoon of flour and 500 ml of heavy cream.
8. Pour this mixture into the gratin dish.
9. On top, break the other half of the eggs and sprinkle with grated gruyère cheese.
10. Bake in the oven (200°C) for 30 minutes.