Beat eggs and milk in a shallow dish. Mix flour, salt and cayenne pepper in another shallow dish or on a piece of wax paper. Dredge catfish fillets in flour mixture, then in egg mixture and again in flour. Set aside on a wax-paper lined baking sheet.

Pour oil into a deep fryer or a large, deep skillet and heat to 360°F on a deep-frying thermometer. Place fillets, two at a time, in hot oil and fry for 2 to 3 minutes on each side, or until golden brown and fish flakes easily when tested with a fork. Place on paper towels to drain.

While catfish are frying prepare the sauce. Heat 1 tablespoon of the melted butter in a large skillet over medium heat. Add shrimp and sauté until light pink on both sides; do not overcook. Stir in garlic, ham strips and vermouth.  Mix in cream, half of the green onion, lemon juice, salt and cayenne pepper; cook for 1 to 2 minutes to reduce cream. Remove from the heat and whisk in remaining 2 tablespoons melted butter. 

Place a catfish fillet on each serving plate and top with three shrimp pieces. Arrange ham strips to fill in gaps between shrimp. Spoon sauce onto catfish, and sprinkle with remaining green onion. Garnish with lemon wedges and parsley sprigs and serve.