Remove from the heat and stir in the mustard and pepper. Cool 5 minutes.
Place the crabmeat in a large bowl. Gently stir in the scallion mixture. Form uniform cakes by placing spoonfuls of the crab mixture on a cookie sheet. Immediately place in refrigerator to harden, about 2 hours.
When ready to serve, beat the eggs in a shallow bowl and place the bread crumbs in another shallow bowl. Melt 1 tablespoon butter and 2 tablespoons oil in a large skillet over medium heat. Working with half of the crab cakes at a time (keep remaining cakes in the refrigerator), dip each cake into the beaten eggs and coat with crumbs. Saute until browned, 2 to 3 minutes on each side (turn cakes only once or they will break up). Drain on paper towels and serve immediately.