Season salmon with fine sea salt and pepper.
Heat cooking spray or 1 tablespoon of neutral oil in a large ovenproof skillet over medium-high.
Cook salmon, skin side down, undisturbed, until salmon skin is crisped and browned, 3–4 minutes. Gently turn fillets and cook until salmon is just opaque at the center, 1–2 minutes for medium rare.
Divide fillets among plates, skin side up, and serve with cucumber-yogurt sauce and carrot salad. Drizzle with neutral oil and sprinkle with flaky sea salt.