Preheat the oven to 400 degrees F.
Line a rimmed baking sheet with foil and place a rack on top. Arrange the bacon on the rack in a single layer. Bake until browned and crisp, 20 to 25 minutes. Let cool, then break the bacon in half.
Meanwhile place the eggs in a large saucepan and cover with cold water by 1 inch. Bring to a boil over medium-high heat. Boil for about 30 seconds, then turn off the heat, cover the pan and let stand 20 minutes. Drain, add cold water and let stand in the cold water for 5 minutes. Drain, peel the eggs and chop.
Combine the eggs with the mayonnaise, onion, relish, Dijon, paprika, celery, 1/2 teaspoon salt and pepper to taste in a bowl. Stir, mashing the eggs slightly, until very well combined. Season with additional salt and pepper.
Lay out 4 slices of toast and top evenly with half of the egg salad, bacon, lettuce and tomato. Sprinkle the tomato with salt. Add another piece of toast to each and top with the remaining ingredients. Close the sandwiches with the last 4 pieces of toast. Use a sharp knife to trim the crusts from the sandwiches; cut in half diagonally.