Peel and devein fresh shrimp. Finely chop in a food processor until minced.
In a large bowl, mix minced shrimp with mayo, lemon juice, breadcrumbs, grated Parmesan cheese, chopped dill, and a beaten egg.
Add Old Bay seasoning, paprika, garlic powder, and black pepper. Adjust to taste.
Incorporate Worcestershire sauce for depth. Mix until well combined.
Divide the mixture into 6 portions. Shape each into burger patties.
Heat a skillet over medium-high heat. Add butter and sear patties on both sides until golden brown (3-4 minutes per side).
Transfer seared patties to a preheated oven (350°F/180°C) for 8-10 minutes to ensure thorough cooking.
Toast burger buns. Place shrimp patty on the bun and add preferred toppings and sauce, like lettuce, tomato, and avocado. Serve hot.