While the chicken stock is preheating in one pot, melt the butter in another large, heavy-bottomed soup pot. Add the leeks, onions, thyme, bay leaves, garlic, 1/2 teaspoon salt and 1/2 teaspoon ground white pepper, and saute over medium heat until the vegetables are wilted, about 10 minutes. Add the preheated chicken stock to the vegetables and bring to a boil. Reduce to a simmer and cook 30 to 35 minutes.
Add the potatoes, return the soup to a boil, then reduce to a simmer again. Continue to cook 20 minutes more, or until the potatoes are tender. Remove the bay leaves. Salt and white pepper to taste, and serve with croutons of French bread toasted with olive oil.