1. Preheat your oven to 400°F (200°C). Line a large rimmed baking sheet with parchment paper or lightly grease it to prevent sticking.
2. In a small bowl, whisk together the melted butter, minced garlic, lemon zest, lemon juice, dried oregano, salt, and pepper. This mixture will be your flavorful sauce that ties everything together.
3. Place the halved baby potatoes on one side of the sheet pan. Drizzle with olive oil and season with salt and pepper. Toss to coat evenly. Roast the potatoes for 15 minutes—this gives them a head start since they take longer to cook than the salmon and green beans.
4. After 15 minutes, remove the pan from the oven. Push the potatoes to one side, then add the salmon fillets skin-side down (if using skin-on) and the green beans to the other side of the pan.
5. Brush the lemon garlic butter mixture generously over the salmon and green beans. Be sure to coat each fillet well; the butter helps keep the salmon moist and adds a wonderful flavor.
6. Return the sheet pan to the oven and roast everything together for 12-15 minutes, or until the salmon flakes easily with a fork and the green beans are tender-crisp.
7. For a golden finish, you can switch the oven to broil for 2-3 minutes at the end—just keep a close eye to avoid burning. This step is optional but adds a lovely touch of color and texture.
8. Remove from the oven and let rest for a couple of minutes. Garnish with fresh parsley before serving if you like.

One little trick I learned from my early cooking experiments—as silly as it sounds—is that resting salmon for a few minutes after cooking allows the juices to redistribute. I remember many a time trying to rush meals along and ending up with dry fish. Patience really does pay off here!