Heat the oven to 350 degrees F. Remove the soft centers of the baguette, leaving a 1/2-inch shell. Put the bread, cut-side up, on a baking sheet and brush with the butter. In a small bowl, combine the mayonnaise, mustard, and Tabasco sauce.
Heat about 3 inches of oil in a medium saucepan until it reaches approximately 360 degrees F. In a medium bowl, combine the milk and the egg. In another bowl, combine the bread crumbs with the salt, black pepper, and cayenne. Dip the shrimp into the flour, then into the egg mixture, and then into the bread crumbs.
Put about a third of the breaded shrimp into the oil and fry, turning, until golden on the outside and just done in the center, 2 to 3 minutes. Drain on paper towels. Repeat with the remaining two batches of shrimp.
Meanwhile, bake the pieces of baguette until crisp, about 5 minutes. Spread the sauce on both sides of the bread. Sandwich the lettuce, tomato, and fried shrimp between the bread.