Season the top of fish fillets with salt (generously). Fish fillets will have skins on the bottom - no need to season the skins.
In a large skillet,heat 2 tablespoons of olive oil on medium heat until heated but not smoking. Add fish fillets skin side up - flesh side down. Cook the flesh side of the fish for about 3-5 minutes on medium heat, until lightly browned.
Flip the fillets over to the other side, skin side down (add more oil, if needed). Cook for another 2-4 minutes on medium heat.
Remove the skillet from heat, close with the lid, and let the fish sit for 5-10 minutes, covered, in the skillet, until flaky and cooked through completely.
Remove fish from pan. Add diced garlic, lemon juice, and white wine to the same pan with oil. Cook on medium-low heat for about 1 minute, until garlic softens a bit. Remove from heat. Add 1 tablespoon of chopped parsley, and 2 tablespoons of butter, turn off heat, to the sauce, stirring, until the butter melts and forms a creamy mixture.
Add fish back to the pan, spoon sauce over the fish, top the fish and sauce with the remaining 1 tablespoon of parsley, and serve.