My Mother's Praised Chicken

large chicken, preferably organic

garlic flavored oil

Scant 1/2 cup white wine or dry white vermouth

to 3 leeks, cleaned, trimmed, and cut into approximately 2-inch logs

to 3 carrots, peeled and cut into sticks

to 2 celery stalks, sliced

Approximately 2 quarts cold water

bouquet garni (mixed herb sachet or bag) or 1 teaspoon dried herbs

Fresh parsley stalks or few sprigs, tied or banded together

kosher salt or 1 teaspoon table salt

red peppercorns, or good grinding pepper

Chopped parsley leaves, from stalks, for serving

Chopped fresh dill, for serving

English mustard, for serving