Heat the broiler to high and line a rimmed baking sheet with aluminum foil.
Add the tuna, chopped eggs, celery, dill pickles, pickled jalapeños and scallions to a mixing bowl. Mix to incorporate and to break up any large chunks of tuna. Set aside.
Add the mayonnaise, mustard and smoked paprika to a small bowl. Whisk to combine. Add the mayonnaise mixture to the tuna mixture and use a rubber spatula to mix until evenly combined. Season to taste.
Arrange the bread on the foil-lined baking sheet. Divide the tuna mixture evenly among the slices of bread. Top the tuna with a few slices of tomato. Sprinkle the tomato with salt and pepper. Top the tomatoes with the pepper jack cheese.
Transfer the baking sheet to the broiler and broil until the cheese is bubbling and melted, 1 to 2 minutes.
Transfer the sandwiches to a cutting board, then slice in half and serve immediately.
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