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Arrange a rack in the middle of the oven and heat to 425°F. While the oven heats, marinate the salmon and soak the onions (instructions below).
Whisk the olive oil, vinegar, lemon juice, garlic, oregano, salt, and pepper together in large bowl. Transfer 3 tablespoons of the vinaigrette to a baking dish large enough to hold all the pieces of salmon in one layer. Add the salmon, turning them over gently a few times to evenly coat in the vinaigrette. Cover and refrigerate. Place the onion and water in a small bowl and set aside for 10 minutes to make the onion less potent. Drain and discard the liquid.
Uncover the salmon and roast until it is cooked through and flakes easily, 8 to 12 minutes. An instant-read thermometer into the middle of the thickest fillet should register 120°F to 130°F for medium-rare, or 135°F to 145°F if you prefer it more well-done. Total cook time will depend on the thickness of salmon, based on the thickest part of the fillet. Meanwhile, compose the salad.
Add the lettuce, tomato, cucumber, olives, and drained red onion to the bowl of vinaigrette and toss to evenly coat. Divide between 4 plates or shallow bowls. When the salmon is ready, place 1 fillet on top of each salad. Sprinkle with the feta and serve immediately.