Preheat the oven to 400 degrees F.
Heat the olive oil in a large cast iron skillet set over medium high heat. Season the salmon with salt. Add the fish to the skillet flesh-side down and sear on both sides until lightly browned, about 2 minutes per side (It won’t be cooked through). Remove to a plate and set aside.
Add the butter or ghee to the skillet, along with the lemon slices and capers. Sauté until the lemon and capers are slightly frizzled and browned, 3 minutes (be careful not to burn the capers). Remove the lemon to the plate with the salmon (you can leave some of the capers behind).
Drizzle a little more oil in the pan, if needed, then add the garlic, shallot and orzo. Cook for about 2 minutes, until the garlic is very fragrant and turning golden brown. Deglaze the pan with the wine and cook until evaporated by half, 2 minutes. Fold in the spinach, until wilted, then add the chicken or fish broth, lemon juice and ½ teaspoon salt. Bring to a simmer, stirring frequently. Transfer to the oven and bake, uncovered for 7 minutes or until the pasta had doubled in size and is al dente. Remove from the oven and nestle the salmon into the orzo and top with the lemon slices. Return to the oven for 3 to 5 minutes, or until the salmon is cooked through.
Garnish with the parsley and serve directly in the pan family-style.