For the Mexican shrimp burgers: Measure out 3/4 cup of the shrimp and set aside. Add the remaining shrimp to a food processor fitted with the blade attachment. Add the cilantro and eggs and pulse until the mixture is combined but not completely smooth. Transfer to a mixing bowl and set aside.
Roughly chop the reserved shrimp into small pieces, then add it to the mixing bowl. Add the breadcrumbs, chipotle adobo sauce, lime juice, salt, pepper and garlic and mix to blend the ingredients. Use a 1/2-cup measure to scoop and shape the shrimp mixture into 4 burgers. They will be sticky. Refrigerate for 30 minutes.
For the avocado aioli: Add the mayonnaise, lime juice, garlic, avocado and some salt and pepper to a food processor and blend until smooth.
Coat the bottom of a large saute pan with the oil and place it over medium-high heat. Once it's very hot, saute the shrimp burgers until just cooked through, 2 to 3 minutes per side. They should be golden brown.
Add about 1 tablespoon of the avocado aioli to each half of the toasted buns. Add a burger to each, followed by a couple of tomato slices and a piece of lettuce. Close the burgers and enjoy!