In the bowl of a food processor, add the habanero, lime juice, cilantro, mayonnaise, carrot, egg, bread crumbs, salt, pepper, and a quarter pound of the shrimp. Pulse until completely smooth. Add the remaining shrimp and pulse a couple times, until you have a coarse ground meat mixture.
Cover a small sheet pan or tray with wax paper. Put some lukewarm water in a bowl and use it to wet your hands as you shape the mixture onto 6 burger patties. Place them on the prepared baking sheet, cover with plastic wrap, and refrigerate for at least 15 to 30 minutes.
Heat a grill or grill pan on medium heat. Generously brush the shrimp burger patties with oil and sprinkle with salt. Place on the grill or grill pan and cook for about 5 minutes per side, until browned on both sides and the color inside has changed to a darker pink.
Lightly toast the buns in the oven or on a heated skillet. On the bottom half, place a lettuce leaf, some habanero tarter sauce, a shrimp burger, a couple slices of bacon, a couple slices of avocado, more tartar sauce to taste, and top with the top bun. Repeat with the rest of the burgers.