Cut bell peppers in half lengthwise, and discard seeds and membranes. Place bell pepper halves, skin sides up, on a foil-lined baking sheet, and flatten with hand. Broil 15 minutes or until blackened. Place in a zip-top plastic bag; seal. Let stand 15 minutes. Peel.
Place bell pepper, mayonnaise, basil, capers, salt, and garlic in a food processor; process until smooth.
Heat oil in a large nonstick skillet over medium-high heat. Sprinkle crabs with Cajun seasoning. Dredge crabs in cornmeal. Add crabs to pan; cook 3 minutes on each side, gently pressing body and legs against pan.
Spread 1 tablespoon mayonnaise mixture evenly over each slice of bread. Arrange 1 crab over each bottom half of bread. Top each crab with 1 lettuce leaf and 1 red onion slice. Cover with top halves of bread.