Rest the cabbage: Finely shred the cabbage and toss it with the sugar, salt and lemon juice. Leave it for 10 minutes. It will soften and release some liquid — that's exactly what you want.
½ a medium cabbage, 1 teaspoon sugar, 1 tablespoon lemon juice
Cook the base: Heat the olive oil and butter in a large skillet over medium heat. Add the onion and cook for 5 minutes until soft. Add the carrot and cook for another 2 to 3 minutes. Pour in the tomato juice, cook for 2 minutes, then stir in the cream or sour cream.
1 medium onion, 1 medium carrot, 2 tablespoons olive oil, 2 oz butter, 4 tablespoons chopped tomatoes , 3 tablespoons cream or sour cream
Add the cabbage: Squeeze any excess liquid from the rested cabbage, then add it to the pan. Cook for 10 minutes, stirring every few minutes, until tender and starting to colour at the edges.
Add the eggs: Whisk the eggs with the garlic, salt, pepper and paprika in a bowl. Pour evenly over the vegetables and scatter the dill or parsley on top.
4 eggs, 2 cloves garlic, Salt, pepper, and paprika, Fresh dill or parsley
Set the frittata: Reduce the heat to low. Cook undisturbed for 10 to 12 minutes until the eggs are fully set and the edges are golden. If the top is still wet, cover with a lid for the last 2 minutes.
Rest and serve: Leave it in the pan for 2 to 3 minutes before slicing. Serve warm or at room temperature.
Video
Notes
Salt the shredded cabbage and leave it for 10 minutes before cooking. It draws out moisture and stops the frittata turning watery.Low heat is essential once the eggs go in. If you rush it with high heat, the bottom burns before the top sets.Reheat leftovers in a dry pan, not the microwave. Two minutes each side brings the edges back to crisp.