Bring a very large stockpot of water to a boil. Prepare a large bowl of ice water. Add half of the collard greens to the boiling water, a little at a time, and push them down into the water. Let the water return to a boil, then cook until tender, about 10 minutes. Using tongs, transfer the greens to the bowl with the ice water to reserve. Repeat with the remaining greens. Drain the greens very well and squeeze them dry in a kitchen towel, then finely shred.
In a very large skillet, melt the butter. Add the shallots and garlic and cook over moderate heat until softened, about 6 minutes. Stir in the cream and simmer, stirring occasionally, until reduced by half, about 25 minutes. Add the greens to the cream and toss until warmed through, about 3 minutes. Season generously with nutmeg and salt and pepper. Add to serving dish and sprinkle with the Parmesan.
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