1. For crab cakes, pulse bread in food processor to fine crumbs. Whisk together the 1/3 cup mayonnaise, red sweet pepper, green onion, 1 tablespoon lemon juice, egg, parsley, mustard, 1/2 teaspoon salt and the ground red pepper in a medium bowl. Gently fold in crab, then the fresh crumbs. Cover with plastic wrap and refrigerate 2 hours, until cold.
2. Meanwhile for caper mayonnaise, combine the 1/4 cup mayonnaise, 1 teaspoon lemon juice, capers, and 1/8 teaspoon salt in a small bowl. Cover and refrigerate up to 24 hours.
3. Spread dry breadcrumbs in a 9-inch pie plate. Lightly pack a level 1/2-cup measure with crab mixture and drop onto breadcrumbs; press lightly and gently turn to coat all sides and shape into a 3x1-inch-thick cake. Place on a cookie sheet. Repeat to form 6 cakes total.
4. Heat oven to 350 degrees F. Heat 1 tablespoon of the oil in a large nonstick skillet over medium heat. Add 3 crab cakes and cook 2 minutes per side, until browned and crisp. Transfer to a cookie sheet. Wipe out skillet. Repeat with remaining 1 tablespoon oil and crab cakes. Bake crab cakes 8 to 9 minutes (12 to 14 minutes, if refrigerated), until heated through.
5. Spread roll tops with caper mayonnaise. Arrange crab cakes on roll bottoms; top with tomato and roll tops. Makes 6 sandwiches.