Begin by cooking the shrimp. In a pot of boiling salted water, cook the shrimp for about 2-3 minutes until they turn pink. Drain and let cool. Chop the shrimp into small pieces.
In a large mixing bowl, combine the chopped shrimp, mashed potatoes, 1/2 cup breadcrumbs, Parmesan cheese, parsley, garlic powder, onion powder, salt, and black pepper. Mix until well combined.
Form the mixture into small balls or patties, about 1-2 inches in diameter. Place them on a baking sheet lined with parchment paper.
In a shallow dish, beat the egg. In another shallow dish, place additional breadcrumbs for coating. Dip each croquette in the egg, then roll in the breadcrumbs to coat.
In a large skillet, heat about 1 inch of oil over medium heat. Once hot, carefully add the croquettes in batches, frying for about 3-4 minutes on each side until golden brown. Remove and drain on paper towels.
Serve warm with your favorite dipping sauce.