Cut meat into 12 even pieces; pound to 1/4 inch thickness. Saute onion, celery, and carrot in 1/4 cup of oil in a large skillet; turn into a large bowl. Add bread cubes, salt, pepper, and thyme; mix until bread cubes are thoroughly moistened.
Place 1/3 cup stuffing on each piece of meat; roll up, jelly-roll fashion; secure with wooden picks. Dredge in flour. Brown beef rolls, a few at a time, in remaining 1/4 cup oil in a large skillet; remove to plate when browned. Drain off pan drippings. Stir in vinegar, water, beef broth, and brown sugar. Add bay leaf, allspice, peppercorns, and cloves tied in a small piece of cheesecloth. Bring mixture to boiling. Return beef rolls to skillet; cover. Lower heat. Simmer 1 hour or until tender when pierced with a fork. Remove spice bag; stir in gingersnaps.
