Place the chick peas and their soaking liquid in a large saucepan and add enough water to cover by 2 inches. Add the bay leaf and bring to a boil. Reduce the heat, cover and simmer 1 hour. Add salt to taste and continue to simmer until the chick peas are tender, 30 minutes to an hour. Remove the bay leaf.
Step 2
Meanwhile, place the red onions in a bowl and cover with cold water. Soak 5 minutes, then drain and rinse. Dry on paper towels.
Step 3
Make the dressing. Mix together the lemon juice, vinegar, mustard, garlic, salt, and pepper. Whisk in the olive oil (or the oil and buttermilk or yogurt). Set aside.
Step 4
When the beans are tender, add the broccoli. Turn up the heat, cover and simmer or steam (depending on how much water is left in the pan) 5 minutes, until the broccoli is tender but still bright. Drain the beans and broccoli and toss with the dressing. Add the herbs and the Parmesan, toss again, and serve warm.