Season salmon fillets with 1 tsp salt.
Heat the oil in a pan over medium-high heat until hot and shimmering. Cook the salmon until golden and crisp on the outside, about 4 minutes.. Carefully flip the fillets and reduce the heat to medium..
Continue cooking until done to your liking, 1 to 2 minutes more, depending on how well done you like your salmon., Remove the salmon and place on a plate. Set aside.
Return the pan to medium heat and add butter, garlic, and a pinch of salt. Cook, stirring often, about 1 minute. Add the white wine and simmer until the sauce is reduced by about half. Add the, lemon juice, capers, lemon zest and fresh oregano. Place salmon back in the pan and heat for an extra minute. Then, spoon the sauce over the salmon. Garnish with additional oregano and serve warm.