1. In 5-quart Dutch oven over medium-high heat, in hot olive oil, cook veal rump roast until well browned on all sides; remove meat to plate. In drippings remaining in Dutch oven, over medium heat, cook celery, onion, and garlic, stirring occasionally, until tender, about 5 minutes. Return meat to Dutch oven; add wine, 8 anchovy fillets, bouillon, pepper, basil, and 1 tablespoon capers; heat to boiling. Reduce heat to low; cover and simmer about 2 hours, turning meat occasionally, until meat is fork-tender.
2. Remove meat from Dutch oven; wrap and refrigerate until chilled. Over medium-high heat, cook mixture remaining in Dutch oven until reduced to about 2 cups. Strain mixture, discarding vegetables. (There will be about 3/4 cup broth.)
3. In blender at low speed (with center part of cover removed) or in food processor with knife blade attached, blend broth and tuna with its oil until smooth; pour into small bowl; cover and refrigerate (mixture will become thick).