Break chicken down into leg quarters, neck, and bone-in breasts with wings attached.
Place chicken pieces, chicken wings, onions, carrots, celery, parsley, and peppercorns in a large stockpot; pour in water.
Bring to a simmer over medium-high.
Reduce heat to medium-low and very gently simmer, uncovered, adjusting heat as needed to maintain a low simmer, until stock is light golden, has some body, and has a rich chicken flavor, about 1 hour 45 minutes.
Remove chicken pieces from stock, and pull off meat; discard bones and skin.
Reserve chicken meat for another use.
Strain stock through a fine mesh strainer into a large (4-quart) heatproof container; discard solids.
Use stock immediately or refrigerate, uncovered, until completely chilled, about 2 hours.
Cover stock and refrigerate for up to 3 days or freeze for up to 4 months.
