In a large bowl, combine 1/3 cup bread crumbs, green onions, red pepper, egg, mayonnaise, lemon juice, garlic powder and cayenne; fold in crab.
Place remaining bread crumbs in a shallow bowl. Divide crab mixture into 6 portions. Gently coat with bread crumbs and shape into 1/2-in.-thick patties.
In a large nonstick skillet, heat butter over medium-high heat. Add crab cakes; cook until golden brown, 3-4 minutes on each side.
For the remoulade, in a bowl, stir together all ingredients until blended.
On each bun bottom, layer a crab cake, lettuce, tomato, onion and remoulade. Replace tops; serve with lemon wedges, if desired.