Clean the hen (or chicken) and place it in a large pot. Add the roughly chopped onion, celery, one leek, two garlic cloves, and the herb bouquet. Cover with cold water until the chicken is fully submerged.
Bring slowly to a boil, reduce the heat to a minimum, and simmer covered for about 1.5 hours. Skim off any foam that forms on the surface during cooking. Remove the chicken from the broth and set it aside.
In the strained broth, add the chopped carrots, the remaining leek, and the whole potatoes. Season with salt and pepper. Cook for about 25-30 minutes until the vegetables are tender. For the last 15 minutes, return the chicken to the broth to warm it up.
First, serve the hot, strained broth, sprinkled with fresh parsley. Then, serve the pieces of meat and the cooked vegetables. Dijon mustard, mayonnaise, or other favorite sauces are great accompaniments to the meal.