Sprinkle coarse salt on the salmon pieces on all sides.
Melt the butter in a large pan over medium heat for about 3 minutes until browned. Add the salmon top side facing down and fry for 3-4 minutes until golden. Add the orange juice and lemon zest and turn the salmon over. Cook for another 4-5 minutes, while basting the salmon pieces with the sauce.
Transfer to a plate and top with lemon slices and chopped parsley.