Place the chicken carcass in a large stockpot (at least 8-quart capacity).
Add carrots, celery, onion, and garlic to the pot.
Add thyme, rosemary, bay leaf, peppercorns, and salt.
Pour in cold water, making sure the ingredients are fully submerged. Leave a couple inches of space at the top of the pot to prevent it from boiling over.
Place the pot over medium-high heat and bring to a gentle boil. Once boiling, reduce heat to low to maintain a gentle simmer. Skim off any foam or scum that rises to the surface using a spoon.
Simmer uncovered for 3 to 4 hours. The longer it simmers, the richer the flavor. Check occasionally and add a bit more water if the level gets too low.
Once done, carefully strain the stock through a fine mesh sieve into a large heatproof bowl or container. Discard the solids.
Let the stock cool slightly, then transfer to airtight containers. Chill in the refrigerator until cold. The fat will rise to the top. Skim it off if you want a clearer stock, or leave it for extra richness.
Use immediately, store in the refrigerator for up to 5 days, or freeze for up to 3 months.