1 (2.5-pound) beef chuck roast
2 cloves garlic, thinly sliced
1 teaspoon kosher salt
½ teaspoon ground black pepper
3 tablespoons vegetable oil
1 cup diced onion
½ cup diced carrot
1 cup beef stock
1 cup chicken stock
2 tablespoons Worcestershire sauce
1 tablespoon hot sauce
2 sprigs fresh thyme
1 dried bay leaf
1 cup mayonnaise
4 (6- to 8-inch) loaves French bread, split lengthwise
1 cup shredded iceberg lettuce
1 large beefsteak tomato, sliced