Combine crabmeat, prosciutto, and breadcrumbs in a bowl. Toss gently.
Stir together egg and next 3 ingredients in a small bowl. Gently fold egg mixture into crabmeat. Cover and chill at least 1/2 hour. Shape mixture into 12 patties, using a scant 1/4 cupful for each. Place patties on a wax paper-lined baking sheet; cover and chill at least 1 hour.
Cook 6 patties in 1 tablespoon butter and 1 tablespoon oil in a large nonstick skillet over medium-high heat 5 to 6 minutes on each side or until browned. Remove from skillet; set aside, and keep warm. Repeat procedure with remaining patties, butter, and oil. Serve warm with Red Pepper Mayonnaise. Garnish, if desired.