Step 1
Preheat oven to 350 degrees F (175 degrees C).
Step 2
Place morel mushrooms in a dry skillet over medium heat and sprinkle with salt and black pepper. Cook stirring often until the mushrooms release their juice and the juice evaporates about 5 minutes.
Step 3
Sprinkle halibut fillets with salt and black pepper on both sides.
Step 4
Heat butter in a large skillet over medium-low heat and cook the halibut fillets until golden brown on the outside about 2 minutes per side. Remove fish from skillet and set aside.
Step 5
Cook and stir garlic scapes in the same skillet used to cook fish until fragrant about 1 minute. Remove pan from heat and stir morel mushrooms and thyme with the garlic scapes until combined.
Step 6
Fold a piece of parchment paper in half crosswise. Use scissors to cut a very large valentine-like heart shape out of the folded paper as large as possible. Repeat with remaining parchment to make 4 large heart shapes.
Step 7
Open the heart shapes; brush right sides of the hearts with canola oil.
Step 8
Place 1/4 morel mushroom mixture in the left (unoiled) half of each heart. Place a halibut fillet on the mushroom mixture. Sprinkle fish with salt and black pepper.
Step 9
Fold the oiled right half of the heart over the fish. Fold about 1/4 inch of parchment paper over starting at the rounded end and work your way down to the point folding as you go. Fold the edge over a second time to enclose fish and mushrooms in a bundle with a double-folded sealed edge.
Step 9
Leave about 1/4 inch of the bottom point unfolded.