Croquettes originated in France, where the verb 'croquer' means to crunch, and a perfectly cooked croquette definitely crunches. In Cuba, croquettas became popular as an economical way to stretch a small amount of a variety of proteins into a tasty dish.
For the bechamel: In a medium saucepan over medium heat, melt the butter. Once the foam has subsided, add the onion and peppers and cook, stirring, about 5 minutes. Whisk in flour until a paste forms and cook for a couple of minutes while whisking. Slowly add milk in a steady stream to form a thick sauce. Season to taste with salt. Set aside to cool, about 20 minutes.
For the croquettas: In a medium bowl, add crabmeat. Gently toss with lime juice. Set aside.
When the bechamel has cooled, add several spoonfuls to the crab until it just holds together. Shape into balls or ovals about the size of golf balls and chill in the refrigerator about 20 minutes.
In a bowl, add the beaten eggs. In another bowl, combine the flour, breadcrumbs, baking powder, and cornstarch. Dip croquettas first in egg to coat, then roll in the flour mixture. Meanwhile, place oil in a Dutch oven (the oil should be at least 4 inches deep) and heat to 375 degrees F. In batches, fry croquettas until golden brown, about 2 to 4 minutes. Remove the croquettas, drain on paper towels, and season with salt.
While the croquettas are frying, for the dipping sauce, whisk together the mayonnaise, miso paste and chives. Serve the croquettas with the sauce on the side.