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Preheat your oven to 425°F. Line a large sheet pan with parchment paper for easier cleanup.
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In a large bowl, toss the halved potatoes with 1 tablespoon olive oil, salt, and pepper. Spread onto the sheet pan and roast for 20 minutes.
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Meanwhile, whisk together the olive oil, lemon zest, lemon juice, garlic, oregano, parsley, paprika, salt and pepper.
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Pat the salmon dry and spoon about half of the marinade over the fillets.
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After the potatoes have roasted for 20 minutes, remove the pan from the oven. Push the potatoes to one side and add the green beans to the pan. Drizzle the green beans with a little olive oil and toss lightly.
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Place the salmon fillets onto the sheet pan and drizzle the remaining marinade over the vegetables.
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Roast for another 12–15 minutes, or until the salmon flakes easily with a fork and reaches your desired doneness.
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Finish with fresh herbs, feta, lemon slices, or red pepper flakes if desired.
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Store leftovers in an airtight container in the refrigerator for up to 3 days. The salmon is delicious cold over salads the next day too.