Using an electric blender or wire whisk, beat together mustard, lemon juice and egg until thoroughly combined. While beating vigorously, gradually pour 4 tbs. of olive oil into the egg mixture in a thin stream. When smooth and creamy, stir in salt and pepper.
Gently fold in crabmeat, then bread crumbs and cayenne pepper. Shape into 8 patties, each about a half-inch thick. They will want to fall apart, but that's the idea of a good crab cake. You want only enough non-crab stuff to just barely bind them.
Melt butter together with remaining 2 tbs. of olive oil in skillet over medium heat. When butter sizzles (but before it burns!) gently ease the crab cakes into the skillet to cook. When well browned (2 to 3 minutes), gently turn and cook other side. Drain on paper towels. Serve immediately with parsley, lemon, tartar, if desired.
Makes 4 main-course servings, 8 appetizers