1. Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper or foil for easy cleanup.
2. Arrange the salmon fillets and asparagus on the prepared baking sheet. Make sure they are evenly spaced to allow even cooking.
3. In a small bowl, mix together the melted butter, olive oil, lemon juice, lemon zest, and minced garlic. Pour this mixture over the salmon and asparagus, ensuring everything is well coated.
4. Sprinkle the dish with salt, pepper, and dill. I like to use my hands to gently massage the seasonings into the fish and vegetables, a trick I learned from watching my mother cook.
5. Bake in the preheated oven for 12-15 minutes, or until the salmon is opaque and flaky when tested with a fork, and the asparagus is tender-crisp.
6. Remove from the oven and let it rest for a couple of minutes before serving, allowing the flavors to meld beautifully.

This dish is proof that a few simple steps can lead to something extraordinary. The key here is not to overcook the salmon, a lesson I learned after a few attempts in my early cooking days.