One 16-ounce bag of edamame is enough for both puree and salad; cook it all at once, and then divide it accordingly.
Make the salad: Combine edamame, bell pepper, sesame seeds, lime juice, chili paste, salt, and pepper.
Make the puree: Process edamame, lime juice, water, mint, garlic, salt, and pepper in a food processor until smooth. (The puree should be warm from the just-cooked edamame; reheat it in a saucepan over low heat if necessary.)
Make the scallops: Season both sides of each scallop with salt and pepper. Heat oil in a large nonstick skillet over medium-high heat until very hot but not smoking. Add scallops, and cook until golden brown, 1 to 2 minutes per side.
Divide warm edamame puree among serving plates. Top with scallops and salad, and serve with lime wedges.