In a food processor, pulse the shrimp until coarsely chopped. Transfer to a mixing bowl.
In a separate bowl, combine breadcrumbs, flour, egg, mayonnaise, Dijon mustard, garlic powder, paprika, salt, and black pepper. Mix well.
Fold the breadcrumb mixture into the chopped shrimp until fully combined. Stir in the green onions.
Form the shrimp mixture into 4 equal patties.
Heat oil in a large skillet over medium-high heat. Once hot, carefully add the shrimp patties. Fry for about 3-4 minutes on each side or until golden brown and cooked through.
Remove the patties and drain on paper towels.
Toast the hamburger buns lightly in the same skillet.
Assemble the burgers by placing a shrimp patty on the bottom bun, adding lettuce, tomato slices, and a generous dollop of tartar sauce. Top with the other half of the bun.