Combine 1 tablespoon Dijon mustard and next 8 ingredients in a medium bowl; stir well with a whisk. Cover and chill.
Combine remaining 1 tablespoon Dijon mustard, mayonnaise, and next 3 ingredients in a large bowl; stir with a whisk. Gently fold in 1/4 cup breadcrumbs and crabmeat. Shape mixture into 12 (1/2-inch-thick) patties. Dredge patties in remaining 1 cup breadcrumbs. Coat both sides of patties with cooking spray.
Heat 2 teaspoons oil in a large nonstick skillet coated with cooking spray over medium heat. Add 6 patties, and cook 4 minutes on each side or until browned. Remove from pan; keep warm. Repeat procedure with remaining 2 teaspoons oil and patties. Serve over greens; drizzle with dressing.