Prepare shrimp by peeling, deveining, and chopping into small pieces. Set aside.

In a large mixing bowl, combine chopped shrimp, breadcrumbs, egg, green onions, lemon juice, zest, salt, and pepper without overmixing.

Form the mixture into one-inch thick patties and chill for 30 minutes.

In a skillet, heat olive oil and cook patties for about 4 minutes on each side until golden brown.

Make the lemon aioli by whisking together mayonnaise, minced garlic, lemon juice, salt, and pepper.

Serve the shrimp cakes with the aioli drizzled on top or on the side.