For the shrimp burgers: Coarsely chop half of the shrimp. Put the remaining shrimp in a food processor and pulse until smooth. Combine both shrimp in a large bowl with the breadcrumbs, lemon juice, salt, garlic powder, pepper, scallions and egg and mix. Refrigerate for 10 minutes, and then form into 4 patties. Refrigerate 10 more minutes.
Heat the oil in a large cast-iron skillet over medium-high heat. Cook the burgers, about 3 minutes per side.
For the Old Bay mayo: Combine the mayonnaise and Old Bay to taste in a small bowl.
To serve, spread the buns with the mayo and place the burgers on the buns. Top the burgers with the avocado slices, lettuce leaves and tomato slices.