For the clearest stock, simmer over very low heat and don't stir.
Heat oven to 400 degrees. Rinse and pat bones dry. Place in a roasting pan and roast for 20 minutes, or until they begin to brown.
Add carrots, celery, onion, and tomato paste and continue roasting, stirring occasionally, for 30 minutes more, or until brown and caramelized.
Transfer bones and vegetables to a stockpot. Skim off and discard fat from pan; add 1 cup water. Cook over medium heat, scraping up brown bits. Transfer to stockpot. Add remaining water and ingredients.
Bring stock to a boil and simmer over very low heat for about 5 hours, skimming often to remove any foam.
Remove pot from heat and let cool slightly. Strain stock carefully through a cheesecloth-lined sieve. Cool completely. Stock can be frozen until needed.