Pat the salmon fillets dry to remove moisture. Sprinkle paprika, oregano, salt, and pepper evenly. Dry fillets give you that golden, crispy sear.
Heat olive oil in a skillet until it shimmers. Place fillets flesh-side down and press gently for 10 seconds. Cook undisturbed for 4 minutes, then flip skin-side down for 1 minute.
In the same skillet, melt butter with 1 tablespoon of olive oil. Sauté garlic for 30 seconds, then sprinkle in flour. Add chicken broth, white wine, lemon zest, juice, and capers. Simmer for 4 minutes until slightly thickened, whisking in the remaining butter.
Nestle salmon back into the sauce and spoon over the top. Warm through for 1–2 minutes. Sprinkle with parsley and serve with extra lemon wedges for brightness.