To prepare crab cakes, heat oil in a large nonstick skillet over medium-high heat. Combine breadcrumbs, onions, crabmeat, and pimiento in a medium bowl. Combine mustard, juice, salt, and egg, stirring with a whisk. Add egg mixture to crab mixture, tossing gently to combine. Divide crab mixture into 4 equal portions, shaping each into a 1-inch-thick patty.
Add crab cakes to skillet; cook 2 minutes. Turn cakes; reduce heat to medium. Cook 3 minutes or until golden brown.
To prepare rémoulade, combine mayonnaise and remaining ingredients, stirring with a whisk. Serve with crab cakes.