Slice the hard boiled eggs in half length-wise and scoop the egg yolks into a small bowl. Use a fork to smash the egg yolks, then add the mayo, mustard, salt, black pepper, paprika and white vinegar. Stir until well-mixed.

Fill each egg half with the egg yolk mixture (do not over-fill them.)

Spread the remaining egg yolk mixture on two slices of toast.

Assemble your sandwiches. Place the naked toast slices on the bottom and top with bacon, lettuce and tomato. Use a butter knife to slice the bottom off of each deviled egg and transfer two for each sandwich. Top with the remaining pieces of toast.