Cook thinner sides of salmon directly under the broiler. If the fish is closer to 1 inch thick, broil it farther away from the heat so the inside of the fish will be done by the time the top is browned.
Preheat the broiler. Line a large baking sheet with foil. In a medium bowl, whisk the mayonnaise, lemon zest, lime zest, and cayenne. Season with salt and pepper. Arrange the fish on the baking sheet; season. Spread the mayonnaise over the fish. Top with the citrus slices. Broil until the mayonnaise and citrus slices are golden brown in spots and the fish is just opaque in the center, 5 to 8 minutes (depending on the thickness of the fish). Garnish with the parsley.