Start by thawing the jumbo shrimp if they are frozen. Once thawed, chop the shrimp into small chunks, aiming for about 1/2-inch pieces.

In a large mixing bowl, combine the chopped shrimp with breadcrumbs, minced garlic, chopped green onions, and the egg. Mix until well combined.

Shape the shrimp mixture into burger patties, roughly 3/4 inch thick. Refrigerate for at least 1 hour.

In a small mixing bowl, mash a ripe avocado and mix with lemon juice, salt, and pepper until smooth.

Heat a non-stick skillet over medium heat, add oil, and cook the chilled shrimp patties for about 3-4 minutes on each side until golden brown.

Assemble the burgers by toasting brioche buns, placing cooked patties on the bottom half, and topping with avocado aioli.