Start by removing any remaining meat from the chicken carcass and set it aside for other recipes or to add back to the stock later.
Place the chicken carcass in a large stockpot.
Add the chopped onion, carrots, celery, garlic, bay leaf, and black peppercorns to the pot.
Cover everything with enough water to submerge the ingredients completely. Make sure to leave some room at the top of the pot to prevent boiling over.
Bring the mixture to a boil over high heat, then reduce the heat to low and let it simmer uncovered for at least 2-3 hours. The longer you simmer, the richer the flavor will be.
Skim off any foam or impurities that rise to the surface with a spoon during simmering.
Once the stock has simmered to your satisfaction and has a rich flavor, remove it from heat.
Strain the stock through a fine-mesh sieve or cheesecloth into a large bowl or another pot to remove the solids. You can discard the solids.
Allow the chicken stock to cool, then refrigerate it. The fat will rise to the top and solidify, making it easy to skim off and discard.
Your homemade chicken stock is now ready to use in soups, stews, sauces, or any recipe that calls for chicken broth or stock.