To make the sauce, combine all of the ingredients in a bowl and stir well. Refrigerate until chilled. The sauce will thicken as it chills.
To prepare the crab cakes, melt 1 tablespoon of butter in a heavy skillet over medium heat. Saute the onion, bell pepper, and garlic until the pepper is limp, approximately 3 minutes. Add the cream, mustard, 1 egg, parsley, cayenne pepper and 1/2 cup bread crumbs, to taste, and mix well. Gently fold in the crabmeat.
Form the mixture into 8 patties, about 1/2-inch thick. In a mixing bowl, combine the remaining 1/2 cup of bread crumbs with the Parmesan. Pat this topping onto both sides of the patties. Refrigerate until firm, about 2 hours.
Using a skillet, combine the oil and remaining 2 tablespoons of butter. Saute the crab cakes in the hot oil-butter mixture for approximately 3 minutes on each side or until golden brown. These crab cakes can also be baked for 7 to 10 minutes in a 400 degree F oven.
To serve, spoon a dollop of the lemon dill sauce along side each crab cake.