To prepare crab cakes, drain crabmeat on several layers of paper towels. Combine crabmeat, bell pepper, and the next 4 ingredients (through egg), tossing gently. Stir in 1/4 cup breadcrumbs. Place remaining 3/4 cup breadcrumbs in a shallow dish.
Divide crab mixture into 8 equal portions. Shape 4 portions into 3/4-inch-thick patties; dredge in breadcrumbs. Heat a large non-stick skillet over medium-high heat. Add 1 tablespoon oil. Add dredged patties; cook 3 minutes on each side or until golden. Remove from pan. Repeat procedure with the remaining crab mixture, breadcrumbs, and oil.
To prepare rémoulade, combine 1/4 cup mayonnaise and remaining ingredients; serve with crab cakes.