Rinse the chicken bones under cold water to remove blood and debris.

Roughly chop onions, carrots, and celery into 2-inch pieces, and slice the garlic head in half crosswise.

Place bones, onions, carrots, celery, and garlic in a large 8–12 quart stockpot and add 16 cups of cold water to cover by about 2 inches.

Set the pot over medium-high heat and slowly bring to a gentle simmer (about 30 minutes); do not allow it to boil.

Skim off any foam or impurities that rise to the surface every 15 minutes during the first hour.

Add thyme, parsley, bay leaves, and peppercorns, gently submerging them in the liquid.

Reduce heat to low and maintain the faintest simmer for 3 to 4 hours, adding hot water if necessary to keep bones covered.

Set a fine-mesh strainer lined with cheesecloth over a large bowl and carefully ladle the stock through, pressing solids lightly to extract liquid.

Cool the strained stock quickly in an ice bath, then refrigerate until the fat solidifies; remove and discard the fat layer.

Transfer cooled stock to airtight containers, leaving headspace if freezing, label with the date, and refrigerate up to 1 week or freeze up to 6 months.