Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
In a food processor, add the shrimp and pulse until finely chopped but not pureed.
In a large bowl, combine the chopped shrimp, mashed avocado, breadcrumbs, green onions, lime juice, garlic powder, salt, black pepper, and cayenne pepper (if using). Mix well.
Add the beaten egg to the mixture and stir until fully incorporated.
Using your hands, form the mixture into small balls, about 1 inch in diameter, and place them on the prepared baking sheet.
Bake in the preheated oven for 15-20 minutes, or until the shrimp bites are golden brown and cooked through.
While the shrimp bites are baking, mix the mayonnaise and cilantro in a small bowl for dipping.
Serve the shrimp and avocado bites warm with the cilantro mayonnaise on the side.