Break the carcass into a few pieces to fit your pot — this exposes more surface area and extracts more flavor.
Place the carcass in a large stockpot or Dutch oven. Add the onion, carrots, celery, garlic, thyme, bay leaves, peppercorns, and parsley stems.
Cover with cold water by about 2 inches.
Bring to a bare simmer over medium heat — small bubbles breaking the surface, not a rolling boil.
Skim any foam or scum that rises to the top in the first 15 minutes.
Reduce heat to low. Maintain a gentle simmer for 3–4 hours.
Taste and season with salt in the last 30 minutes.
Strain through a fine-mesh sieve into a clean pot or large bowl. Press gently on the solids.
Discard the solids. Let the stock cool slightly before refrigerating.
Refrigerate uncovered until the fat solidifies on top.
Skim the fat — save it for cooking or discard.
Transfer to airtight containers. Refrigerate for up to 5 days or freeze for up to 3 months.