Combine the ingredients. Add 5 sprigs parsley, 3 sprigs thyme, 1 celery stalk cut into thirds, 1/2 whole chicken (or 1 breast, 1 leg, 1 wing, and 1 thigh), 1/2 leek, 1/2 cup white wine, 2 teaspoons kosher salt, and 1/2 teaspoon black peppercorns to a large pot. Add enough cold water to cover the chicken by 1 inch.
Poach the chicken. Place the pot over medium heat and bring to a gentle simmer, then reduce the heat so the liquid is barely moving. If using a mix of white and dark meat, start checking with an instant-read meat thermometer after 45–50 minutes. Remove the breast when it reaches 165°F and the leg, thigh, and wing when they reach about 175°F.
Rest and strain. Return any chicken pieces you removed early to the pot and let everything cool in the broth for about 30 minutes. Transfer the chicken to a cutting board, remove the skin and bones, then dice, slice, or shred. Strain the broth through a fine-mesh sieve and refrigerate for up to 4 days or freeze for up to 3 months.