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Cook collards in a large pot of boiling water with 1 Tbsp salt until just tender, 6 to 8 minutes, then drain. Transfer to a bowl of cold water, then spread leaves, undersides up, on paper towels, overlapping cut edges slightly, and pat dry.
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Bring wine to a boil with shallot, garlic, 4 Tbsp butter, 1/2 tsp salt, and 1/4 tsp pepper in a heavy medium saucepan. Add mushrooms and cook, covered, over medium heat, stirring occasionally, until tender, about 12 minutes. Butter a 2-qt shallow baking dish, then strain mushroom juices into baking dish, reserving mushrooms.
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Preheat oven to 450°F with rack in lower third.
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Mound about 1/4 cup mushrooms in center of each collard leaf. Fold leaves to enclose filling and arrange bundles, seam sides down, in 1 layer in baking dish. Dot with remaining Tbsp butter and cover with foil.
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Heat in oven until bundles are hot and juices are bubbling, about 20 minutes.