Heat the oven to 375ºF. Season the chicken legs all over with the salt. Arrange them, skin side up, in a single layer in an ovenproof baking dish with a tight-fitting lid.
Scatter the garlic and celery into the gaps between the chicken pieces, and then drizzle everything with the olive oil. Grind some black pepper and a bit of nutmeg over the chicken and vegetables and arrange the parsley on top.
Pour in the vermouth and the chicken stock. Cover the dish tightly with aluminum foil and put on the lid. Bake the chicken for an hour to an hour and 15 minutes, without removing the lid until the hour mark. When the chicken is really tender, and the garlic is soft enough to spread, remove the dish from the oven.
Serve the chicken in shallow bowls with plenty of the fragrant sauce; spread the softened garlic on the bread and then dunk it into the sauce as you eat your chicken.