Fill a large stockpot with about two quarts water and two teaspoons of the salt. Bring to a boil over high heat.
Remove the pot from the heat, add the shrimp, and cook (off the heat) for 1-2 minutes, until the shrimp are pink/orange and slightly firm.
Use a slotted spoon or skimmer to transfer the shrimp to a colander. Set the shrimp water aside.
Rinse the shrimp under cold water until they are cool enough to handle.
Return the shrimp water to a boil, and then reduce the heat to low so the water simmers calmly.
Add the eggs gently, lowering them to the bottom, two at a time, with a large ladle. Let the eggs cook at a simmer for exactly 14 minutes.
While the eggs cook, peel and chop the shrimp and put them in a large bowl.
Sauté the bacon in a skillet over medium high heat until it is firm and just turning golden brown, 4-5 minutes. Transfer the bacon to a paper towel to drain.
When the eggs are done, transfer them to a strainer and rinse under cold water until they are cool enough to handle, about two minutes. Peel the eggs and cut them in half lengthwise. Separate the whites from the yolks. Coarsely chop the egg whites and add them to the bowl with the chopped shrimp. Press the yolks through a mesh strainer into a medium bowl. Add the mayonnaise, hot sauce, mustard and remaining ½ teaspoon salt to the yolks and whisk until the mixture has the consistency of cake batter, about one minute.
Using a rubber spatula, fold the yolk mixture into the shrimp mixture until the shrimp and egg whites are evenly coated with the deviled-egg dressing.
Season with pepper and more salt if desired, and toss again.
When covered, the shrimp and deviled-egg salad will keep in the refrigerator for two days.
To serve, load two slices of tomato and one leaf of lettuce into each of the top-loading buns and spread ¾ -1 cup of the shrimp and deviled-egg salad into each roll. Garnish each roll liberally with the reserved diced bacon and the scallions.
