Remove outer leaves from the cabbage and rinse it. Cut into quarters, remove the core, and finely shred, removing any tough ribs if needed.
Place the cabbage in a pot, cover halfway with water, and cook until tender. Drain.
Slice the onions. In a frying pan, melt the butter and sauté the onions until translucent. Add the flour, stir well, and cook for a few minutes to make a roux.
Chop the dill finely. Add the cooked cabbage to the pan, mix with onions and roux, add dill, stir well, and sauté for a few minutes. Serve warm.