Beat the eggs with the lemon pepper and garlic salt until blended; set aside.
Stir together ground almonds with 1 cup of Parmesan cheese in a shallow dish until combined; set aside.
Dust the Barramundi fillets with flour shaking off any excess.
Dip the Barramundi in egg then press into the almond mixture.
Melt butter in a large frypan over medium high heat. Cook Barramundi in melted butter until golden brown on both sides; 2 to 3 minutes per side.
Reduce heat to medium and season fillets with salt if desired. Sprinkle the Barramundi with the remaining Parmesan cheese then cover and continue cooking until the Parmesan cheese has melted; about 5 minutes.
Transfer the Barramundi to a serving dish and garnish with parsley springs and lemon wedges to serve.