01 - Preheat oven to 425°F. Arrange beef bones in a roasting pan in a single layer and roast for 30 to 40 minutes, turning once until deeply browned.
02 - Transfer roasted bones to a large stockpot. If using tomato paste, spread it evenly over the bones before adding other ingredients.
03 - Place carrots, celery, onions, and garlic in the roasting pan and roast for 15 minutes until lightly browned. Add vegetables to the stockpot.
04 - Pour a small amount of water into the roasting pan, scrape up browned bits, and add this liquid to the stockpot.
05 - Add bay leaves, peppercorns, thyme, parsley stems, and salt to the stockpot. Pour in cold water to cover all ingredients.
06 - Heat slowly to a gentle simmer over medium heat. Skim off foam and impurities during the first hour.
07 - Reduce heat to low and simmer uncovered for 4 hours, skimming regularly and adding water if needed to keep bones submerged.
08 - Strain liquid through a fine-mesh sieve or cheesecloth into a large bowl, discarding solids.
09 - Allow stock to cool, then refrigerate. Once chilled, remove and discard the solidified fat layer if desired.
10 - Store in airtight containers in the refrigerator for up to 5 days or freeze for up to 3 months.