To make the emulsion: In a food processor with metal blade, pulse the egg, mustard, garlic and lemon juice for 1 minute. In a steady stream, add the 1 cup of oil. Blend until the emulsion is thick. Season with salt and pepper. Set aside covered in the refrigerator until ready to use.
For the crab cakes:
In a saute pan, heat the 1 tablespoon olive oil. When the oil is hot, saute the vegetables until wilted, about 2 minutes. Remove from the heat and cool. In a mixing bowl, combine the crab meat, cooled vegetables, Creole mustard and parsley together. Season with salt and pepper. Fold in 3/4 cup of the emulsion. Stir in enough bread crumbs to bind the cakes, about 1/2 cup. Portion the mixture into 1/2 cup cakes, and set aside on a platter.
Season the flour and remaining bread crumbs with Essence and place in seperate containers. In a small bowl, whisk the egg and milk together. Season the egg wash with Essence. Dredge the cakes in the seasoned flour, then dip the cakes in the egg wash, letting the excess drip off. Dredge the cakes in the bread crumbs.
Fill a saute pan with 1/2-inch vegetable oil. Heat the oil. When the oil is hot, pan-fry the cakes for 2 to 3 minutes on each side, or until golden. Remove from the oil and drain on a paper-lined plate. Season the cakes with Essence. Serve the crab cakes garnished with the brunoise peppers and with the leftover emulsion.
Yield: 8 cakes, about 4 servings