Preheat the oven to 400°F (200°C). Line a large sheet pan with parchment paper or lightly grease it.
In a small saucepan over medium heat, melt the butter. Continue cooking, swirling occasionally, until the butter turns golden brown and smells nutty, about 3-4 minutes. Remove from heat and stir in the lemon zest, lemon juice, and minced garlic. Set aside.
Place the trimmed asparagus and cherry tomatoes on the prepared sheet pan. Drizzle with olive oil, sprinkle with dried thyme, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Toss to coat and spread in an even layer.
Place the salmon fillets skin-side down on the sheet pan among the vegetables. Season the salmon with the remaining 1/2 teaspoon salt and 1/4 teaspoon black pepper.
Pour the lemon brown butter evenly over the salmon fillets and vegetables.
Bake in the preheated oven for 12-15 minutes, or until the salmon is cooked through and flakes easily with a fork, and the vegetables are tender.
Remove from the oven and let rest for 2 minutes before serving. Spoon any pan juices over the salmon and vegetables.