Set up shallow dredging dishes (1 for flour, 1 for eggs, 1 for panko/coconut).

Melt 6 tablespoons butter in microwave in a small bowl. Remove, stir in lime zest and 2 tablespoons cilantro; set aside until ready to use.

Heat a large nonstick pan (you may need to use 2 pans to avoid overcrowding) to medium-high; add 2 tablespoons butter and olive oil.

Pat fish dry with paper towel. Dredge each piece in flour, then egg, then panko/coconut mixture.

Place fish in hot pan; cook 1—2 minutes. Check bottoms and, when nicely brown, flip. Reduce heat to medium and cook approximately 2 minutes, depending on thickness of fish (reduce heat to low to avoid burning if pieces are thick). When fish is opaque and coating is brown, remove from heat.

Transfer to serving plates; spoon butter mixture over fish and top with cilantro.