Preheat the oven to 400°F (200°C).
Line a large baking sheet with parchment paper or lightly grease it with olive oil.
Place the trimmed asparagus on one side of the baking sheet and drizzle with 1 tablespoon olive oil. Toss to coat and spread in a single layer.
In a small bowl, combine the melted butter, fresh lemon juice, lemon zest, minced garlic, chopped parsley, dill, chives, kosher salt, and black pepper. Stir well to create the lemon herb butter sauce.
Place the salmon fillets skin-side down on the other side of the baking sheet.
Brush each salmon fillet generously with the lemon herb butter sauce. Reserve some sauce for later.
Roast in the preheated oven for 12 minutes.
Remove the baking sheet from the oven. Brush the salmon and asparagus with the remaining lemon herb butter sauce.
Return to the oven and roast for an additional 3 minutes, or until the salmon is cooked through and flakes easily with a fork, and the asparagus is tender-crisp.
Remove from the oven and let rest for 2 minutes before serving.
Serve the salmon fillets alongside the roasted asparagus, spooning any remaining lemon herb butter from the pan over the top.