Preheat the oven to 350. Line a baking sheet with parchment paper.

With a sharp knife, make 3 slits, at an angle and about 1 1/2 inches apart, on each side of fish. Rub 1 tablespoon olive oil over each side of fish. Fill cavity with lemon slices, orange slices, and thyme.

Place fish on prepared baking sheet. Combine kosher salt, lemon zest and juice, orange zest and juice, and black pepper in a large mixing bowl. Mix well. Mound the mixture evenly on surface of fish, leaving head and tail uncovered. With your fingers, firmly press mixture into the flesh.

Bake for 1 hour. Remove from oven and let cool for 2 minutes. With the back of a heavy spoon or a mallet, lightly pound salt crust to crack it open, beginning at the tail end. Carefully pull off salt crust. Then, with a small spatula or wide knife, remove flesh from the bone from the top side of the fish. Remove backbone and serve flesh from bottom side of fish. Serve garnished with olive oil and parsley.