This rich stock can be used in a variety of soups and sauces. Reserve the shredded beef and tomato pieces to make Hearty Beef Stew.
Preheat oven to 450 degrees. Arrange ribs in a large roasting pan; sprinkle generously with salt and pepper. Roast 1 1/2 hours, turning ribs halfway through.
Combine 3 quarts water and tomatoes and their juice in a stockpot. Bundle bay leaves, peppercorns, and dill in a small piece of cheesecloth; tie with kitchen twine, and add to pot.
Transfer roasted ribs to pot. Pour off and discard fat from roasting pan. Pour remaining cup water into pan, and place over medium-high heat. Bring to a boil, stirring with a wooden spoon to scrape up any browned bits from the bottom, until water is reduced by half. Transfer liquid and bits to stockpot.
Cover the pot; bring mixture to a simmer over high heat, but do not boil. Reduce heat to a gentle simmer, and place a smaller pot lid directly on surface of stock to keep ingredients submerged; cook until meat is very tender and pulls away from the bone, about 1 1/2 hours. Skim surface with a spoon as needed.
Prepare an ice bath. Remove herb bundle from pot, squeezing out liquid into pot, and discard. Strain stock through a sieve into a large heatproof bowl set in ice bath until stock is room temperature, stirring frequently.
Transfer ribs and tomato pieces to another bowl. When cool enough to handle, pull rib meat from bones, and shred with your fingers. Discard bones. Store meat and tomato pieces in an airtight container in the refrigerator, up to 3 days.
Transfer the cooled stock to airtight containers; refrigerate at least 6 hours or overnight. With a large metal spoon, skim off and discard fat layer that has collected on the top. If storing, leave fat layer intact (it helps to seal in flavor).
Refrigerate stock in airtight containers for up to three days or freeze for up to six months.