Cut several small slits in roast. Stuff garlic slices in slits. Season roast with salt, pepper, and cayenne. Heat oil in a large Dutch oven. When real hot, add roast and brown well on both sides. Remove to a plate. Drain all but 2 tablespoons of oil from pan. Add onions and carrots. Cook 5-10 minutes, or until tender. Empty pan into 5-quart crockpot. Add roast to crock. Add beef and chicken stock. If necessary, add enough water to bring the cooking liquid 3/4 way up the roast. Add remaining ingredients, except bread or buns, lettuce and mayo. Cover and cook on low 6-7 hours, or until meat is tender and falls apart.
Remove meat and carve into thin slices. Meat will begin to shred. Keep meat warm by covering with plastic wrap. Drain liquids from crock pot into a large pot. Remove bay leaf and thyme sprigs. Add bits and pieces of meat from slicing process back into the pot, which will be your debris. Bring to full boil over medium-high heat and reduce until thickened. Season with salt and pepper, if necessary.
Cut French bread into 6-inch sections. Spread mayonnaise to bun top and bottom. Then, add some shredded lettuce on the bottom half. Now add beef slices, then ladle with generously with debris gravy. Serve.