Dry-brine the salmon. Pat the fillets completely dry with paper towels, then season both sides with salt. Set them on a plate, uncovered, and let them sit for 10–15 minutes while you prep everything else. This is the step most sheet-pan salmon recipes skip, and it's the reason this one turns out flakier: salting ahead of time draws a little surface moisture out of the fish, which then reabsorbs and seasons the flesh from the inside instead of just sitting on top. Skip it, and the salmon tends to steam in the oven instead of roast, which is what leaves it pale and a little rubbery.
Preheat the oven to 425°F (220°C). Line your sheet pan with parchment paper.
Toss the vegetables. In a mixing bowl, combine the cherry tomatoes, olives, red onion, capers, garlic, oregano, 1 tablespoon of olive oil, the 1/2 teaspoon salt, and black pepper. Toss well and spread in an even layer on the sheet pan.
Give the vegetables a head start. Roast the tomato mixture alone for 5 minutes before the salmon goes in. This is a small step, but it matters cherry tomatoes need a bit more time than a salmon fillet to actually blister and soften, and starting them solo means you're not stuck choosing between undercooked veggies and overcooked fish.
Add the salmon. Remove the pan, nestle the salmon fillets among the vegetables, and brush the tops with the remaining tablespoon of olive oil. Lay a few lemon slices over each fillet.
Roast until just cooked through. Bake for 10–12 minutes, until the salmon flakes easily with a fork and reaches an internal temperature of 130–135°F for medium (it'll carry over to about 140°F while resting). Pro tip: pull it a touch earlier than you think you should salmon keeps cooking from residual heat once it's out of the oven, and that's usually where the "dry salmon" problem actually happens.
Finish and serve. Squeeze the lemon juice over everything, scatter the feta and parsley on top, and let the pan rest for 2–3 minutes before serving.
