Place a rack in the center of your oven and preheat the oven to 400 degrees F. Generously coat a large rimmed baking sheet with nonstick spray. Arrange the salmon fillets in the center of the sheet.
In a small bowl with a fork, combine the softened butter, garlic, lemon zest, 2 tablespoons chopped fresh parsley, and 1/4 teaspoon black pepper. Mash to create a paste, then rub on the salmon fillets. If desired, arrange extra lemon slices on top.
Place the green beans and tomatoes in a large bowl. Drizzle with olive oil and sprinkle with 1/2 teaspoon kosher salt and the remaining 1/4 teaspoon black pepper. Toss to coat, then arrange around the salmon. Drizzle the lemon juice over the top of the salmon and vegetables.
Place the sheet pan in the oven and cook until the fish flakes easily with a fork and reaches an internal temperature of 135 to 140 degrees F, about 16 to 20 minutes.* Let rest 3 minutes. Sprinkle with remaining 2 tablespoons parsley, then serve, sprinkled with additional salt and/or pepper to taste.
Notes
*The cooking time will vary based on the thickness of your salmon. Thicker (2-inch-plus) slices will need several extra minutes, while thinner slices may cook more quickly. My salmon fillets were a little more than 1 inch thick and cooked in 19 minutes.
To Store. Place leftover salmon in an airtight storage container for up to 1 day.
To Reheat. This recipe is best enjoyed the day that it is made, as salmon usually dries out when reheated. If you have leftover salmon, try serving it at room temperature over a salad the next day or flaking and scrambling it with eggs. Extra veggies can be reheated and mixed into a salad or eggs, or enjoyed on their own.