Mix softened butter with chopped chives and parsley in a wide dish. Season with salt and freshly ground black pepper; mix well with a fork until smooth. Place salmon fillets on top of butter mixture and set aside for 30 minutes, turning fillets after 15 minutes, to allow salmon to absorb the butter mixture.
Cook the salmon slices on both sides on a hot non-stick pan or pan until they are golden brown. To turn them around, use a shovel, so you will avoid breaking them.
Heat a non-stick pan over medium heat; place coated salmon fillets in pan and cook until golden and crisp on one side. Carefully turn salmon fillets over and continue to cook until other side is crisp and salmon is done to your liking.