Preheat oven or barbecue (grill) following instructions below.
Place each salmon fillet in the centre of one 12x18-inch heavy-duty aluminium foil piece. Divide the asparagus into 4 equal portions and arrange next to the salmon on each foil piece.
In a small bowl, mix together the melted butter, lemon juice, garlic and parsley. Pour the garlic/butter mixture evenly over each piece of salmon and asparagus; season with salt and pepper to taste, and top each pack with the parmesan cheese (about 2-3 tablespoons per pack).
Tent with foil, tightly sealing the edges to prevent the butter being leaked, to create a foil packet.
For The Oven:
Bake in preheated oven to 200°C | 400°F for 15 minutes, or until cooked to desired doneness.For a crispy top, broil for 1-2 minutes extra until Cheese is golden.
For The Grill:
Grill, covered on medium high heat for 15-20 minutes, or until cooked to desired doneness.
OPTIONAL: For a crispy top, broil for 1-2 minutes extra until Cheese is golden.
Serve with fresh lemon wedges and garnish with extra parsley.