Burgers:

In a food processor, combine the shrimp, egg, cilantro, garlic, 3/4 cup bread crumbs, poblano chile, salt, and pepper. Process until the mixture is a coarse puree. Form the mixture into 6 patties and set aside (if the mixture is too wet, add additional bread crumbs, 1 tablespoon at a time, until the mixture can be molded easily).

Put a grill pan over medium-high heat or preheat a gas or charcoal grill. Brush the patties with vegetable oil and grill until golden, about 3 minutes per side, depending on the thickness.

Avocado Aioli:

Scoop the avocado pulp into the bowl of a food processor. Add the mayonnaise, lime juice, garlic cloves, serrano chile and cilantro. Process until smooth. Season with salt and pepper, to taste.

To assemble:

Serve the shrimp burgers on buns, topped with a dollop of avocado aioli, sliced tomato, and lettuce.