Pre-heat the oven to 300ºF.
Line a small sheet pan with parchment paper. Drizzle 1 tbsp olive oil in the center of the paper, then place the filet on top of the oil, skin side down. To the top of the fish and also around it, season with salt and pepper, then add the slices of orange and 1/2 the lemon slices. Drizzle the fish and citrus with 1-2 tbsps olive oil and a generous pinch of kosher salt. Put in the pre-heated oven for 15-20 minutes. After 15-20 minutes, turn to broil for about 3 minutes to add some browning.
While fish is baking, add salted butter to a small pot over medium heat. Once melted, add thinly sliced shallot and stir. Bring to a gentle simmer, then add 4-5 very thin lemon slices. Add the chopped olives and stir all together. Bring back to a simmer for about 1 minute, then remove from heat.
Plate the salmon with the citrus slices off the the side. Spoon 2-4 spoonfuls of the lemon olive butter sauce over the fish. Garnish with flakey salt, more black pepper, and chopped parsley.