Working in batches, steam spinach, covered, in a large pot over medium-high heat, stirring occasionally, until wilted, 2 to 4 minutes. Drain. Let cool. Squeeze out and reserve liquid. Chop spinach. (You should have 4 and 1/2 cups.)
Melt butter in a medium skillet over medium heat. Cook shallots until translucent, about 3 minutes. Add flour, and cook, whisking, until raw flour smell is cooked off, 1 to 2 minutes. gradually whisk in milk. Bring to a simmer, and cook for 2 minutes. Season with 1t salt and 1/2t pepper.
Stir in spinach. If mixture is too thick, thin with reserved spinach liquid. Stir in nutmeg. Continue to cook until warmed through. Serve immediately