Sort through dry beans and rinse. Place in a pot with water and bring to a boil and then a gentle simmer until cooked through and tender, about 2 - 3 hours. Drain.
Place all vegetables in a bowl. Remove tail from shrimp and rough chop with a knife or pulse in a food processor (should be chunky). Add shrimp, panko breadcrumbs, minced garlic and 1/3 of the cooked, cooled beans to the bowl.
Add the remaining 2/3 of the cooked black beans into a food processor with the beaten eggs, salt and black pepper. Puree until smooth. Pour pureed beans into the shrimp mixture and toss to combine well. The batter will be slightly wet but will still form into cakes; if too wet, add more breadcrumbs.
Shape into ¼ cup patties. To cook, sprinkle olive oil into a warmed skillet over medium heat and cook about 2-3 minutes per side. Look for a browned crust and check the first one for doneness by cutting it in half.
Mix sour cream and lime juice together for the lime crema. Top shrimp and black bean patties with lime crema.