Soak the white beans overnight in plenty of water. The following day, rinse and simmer covered with 1 liter of water, the bay leaf and 2 chopped garlic cloves for approx. 1 1/2 hours. Then drain and leave to cool.
Meanwhile, clean the green beans, cut off the ends and cook in plenty of boiling salted water for about 8 minutes until al dente. Then rinse in cold water and drain.
Peel and halve the onions and cut into fine rings. Drain the tuna in a sieve and cut into large pieces.
For the dressing, mix the vinegar with the sugar, mustard, salt and pepper. Gradually stir in the olive oil with a whisk. Squeeze in the remaining garlic clove.
Mix the white and green beans, onions and tuna together.
Wash and dice the tomatoes and add to the other ingredients. If desired, add the finely chopped anchovy fillets. Pour over the dressing, sprinkle with the parsley, stir in thoroughly and leave to stand for a while before serving.