Center a rack in the oven and preheat to 450 degrees.
Using a paring knife, slice the peel from the preserved lemon and cut it into small squares. Discard the pulp.
Bring the water and sugar to a boil in a small saucepan, drop in the peel, and cook for 1 minute. Drain and set aside.
Heat 2 tablespoons of olive oil in a large skillet over high heat. Add the vegetables and garlic, season with salt and pepper and sauté until vegetables are brown on all sides. (If necessary, do this in 2 batches.) Spoon vegetables into a 4½- to 5-quart Dutch oven or other pot with a lid and stir in the herbs and the preserved lemon.
Return the skillet to the heat and add another tablespoon of olive oil. Brown the chicken on all sides, seasoning it with salt and pepper as it cooks.
Tuck chicken into the casserole, surrounding it with the vegetables.
Mix together the broth, wine, and the remaining olive oil and pour over the chicken and vegetables.
Put 1½ cups flour in a medium bowl and add enough hot water to make a malleable dough. Dust a work surface with a little flour, turn out the dough, and, working with your hands, roll the dough into a sausage.
Place the dough on the rim of the pot — if it breaks, just piece it back together — and press the lid onto the dough to seal the pot.
Slide the pot into the oven and bake for 55 minutes.
Now you have a choice — you can break the seal in the kitchen or do it at the table, where it's bound to make a mess, but where everyone will have the pleasure of sharing that first fragrant whiff as you lift the lid with a flourish. Whether at the table or in the kitchen, the best tool to break the seal is the least attractive: a screwdriver. Use the point of the screwdriver as a lever to separate the lid from the dough.
Depending on whether your chicken was whole or cut up, you might have to do some in-the-kitchen carving, but in the end, you want to make sure that the vegetables and the delicious broth are on the table with the chicken.