Add the olive oil to a large, heavy-bottomed skillet and heat over medium-high heat. Season salmon fillets generously on both sides with salt and pepper and then place skin-side down into the hot oil. Sear the salmon until the skin is very crisp and browned, about 3 to 5 minutes.
Using a spatula, turn the fillets skin side up and sear the other side until nicely browned, about 2 to 3 more minutes, depending on the thickness of the fillet. Transfer the fillets to a sheet pan or plate and keep warm either in a low oven or covered with aluminum foil.
Discard the oil from the skillet and return to the stovetop over medium heat. Add the white wine and stir, scraping up any browned bits from the bottom of the pan. Let the wine reduce by half.
Add the capers and the optional minced garlic and stir for a minute until heated through. Stir in the butter until it is melted and combined with the wine and capers. Add the fresh lemon juice and season with the salt and pepper to taste.
Remove the skillet from the heat and stir in the chopped parsley. To serve, place the cooked salmon fillet on a plate with your choice of vegetable and starch. Spoon the pan sauce over the fish and serve immediately.
NOTE: To check for doneness, the salmon fillets should be slightly springy when lightly pressed, and not too firm or falling apart. The flesh in the thickest part of the fillet should be very pink but no longer translucent.