How to Make It
Stir together hazelnuts and rosemary on a plate. Sprinkle fillets evenly on both sides with salt. Brush 1 side of each fillet with some of the egg. Place fillets, egg sides down, in hazelnut mixture, pressing lightly to adhere.
Melt 1/4 cup butter in a large skillet over medium-high. Add 2 fillets, hazelnut sides down, to skillet; cook, undisturbed, until browned, about 3 minutes. Carefully flip fillets; cook, spooning butter in skillet over tops of fillets, until fish is flaky and opaque, about 1 minute. Transfer fillets to a plate. Wipe skillet clean. Repeat process with remaining 1/4 cup butter and 2 fillets.
Season fillets with additional salt; serve with lemon wedges.