1. Preheat oven to 400°.
2. Brush tomato paste evenly over the beef bones. Place bones in a shallow roasting pan coated with cooking spray. Bake at 400° for 40 minutes or until slightly charred, turning after 20 minutes.
3. Place bones in a large stockpot. Carefully add 2 cups cold water to roasting pan, scraping pan to loosen browned bits. Pour liquid from pan into stockpot. Add onion and remaining ingredients to pot. Add remaining 10 cups cold water; bring to a boil. Reduce heat, and simmer 2 hours; skim surface occasionally, discarding foam.
4. Strain stock through a fine sieve lined with cheesecloth into a large bowl; discard solids. Cool to room temperature. Cover and chill 8 hours or overnight.
5. Skim solidified fat from surface of stock; discard fat. Place stock in a large saucepan; bring to a boil. Reduce heat, and simmer until syrupy and reduced to 6 tablespoons (about 1 hour and 15 minutes), skimming foam from surface as needed.