Fry the nuts in a dry frying pan until golden brown, for about 3 minutes, stirring occasionally. Remove the pan from the stove.
Steam the Brussels sprouts for about 10 minutes, then add the cauliflower to the double boiler and cook together for another 2 minutes, until both types of cabbage are soft.
Put the cabbage in a large bowl, salt, pepper, and lemon juice, and stir. Sprinkle the cabbage salad with toasted nuts. Serve the cabbage salad immediately.