Add pistachios (reserve a few for garnish) and a pinch of salt to a blender. Pulse until finely chopped—but not powdery. Transfer to a plate.
Pour the buttermilk into a shallow bowl. Season lightly with salt.
Pat halibut dry and season with kosher salt. Dip each filet in the buttermilk, allowing excess to drip off, then press both sides into the chopped pistachios, firmly coating.
Heat a nonstick skillet over medium heat. Add 1 tablespoon butter. Once foaming, gently lay in the halibut. Cook 3 minutes per side or until golden and internal temp reaches 135°F. Transfer to a warm plate.
Wipe out the pan. Add remaining 2 tablespoon butter. Once it begins to brown, turn off heat and stir in capers, chopped parsley, and a squeeze of lemon juice.
Spoon sauce over the halibut, finish with lemon zest and reserved pistachios, and serve immediately.