In a large frying pan over medium heat, cook bacon, turning occasionally, until lightly browned and crisp but not brittle, about 10 minutes. Drain on paper towels.
Meanwhile, in a blender or food processor, combine mayonnaise, parmesan, lemon juice, mustard, garlic, anchovy, salt, pepper, and Worcestershire. Whirl until smooth. Scrape into a small bowl.
Spread Caesar mayo on bread slices. Top half with tomato and sprinkle with sea salt. Add bacon, lettuce, and remaining bread slices. Serve with extra mayo.
Note: Nutritional analysis is per sandwich.