Place ribs, onion, and carrot in a shallow roasting pan. Bake at 400° for 30 minutes or until meat is browned, turning to brown all sides.
Transfer ribs, onion, and carrots to a large stock pot. Add remaining ingredients. Bring mixture to a boil; reduce heat, and simmer, uncovered, for 3 hours. Remove from heat; let cool to lukewarm.
Strain stock, reserving liquid. Discard ribs, vegetables, and spices. Place stock liquid in a container; cover and refrigerate until thoroughly chilled. Lift solid fat from top of stock; discard fat. Use Basic Brown Stock as a base for soups, sauces, or gravies.
Note: Basic Brown Stock may be frozen up to 3 months.