Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Bring about 1 inch of lightly salted water to a boil in a skillet; cook spinach in 2 batches until wilted, 1 to 2 minutes. Drain and rinse spinach under cold water until cool; squeeze small handfuls to remove moisture and coarsely chop.
Heat milk and heavy cream in a saucepan over medium heat, stirring occasionally, until warm.
Meanwhile, melt butter in a large saucepan over medium-low heat; cook and stir shallots until softened, about 5 minutes. Stir in flour and cook for about 3 minutes; add warm milk and cream mixture, whisking constantly. Simmer and whisk until thickened, 3 to 4 more minutes. Stir in spinach and nutmeg; season with salt and black pepper.
Transfer spinach mixture to a baking dish. Sprinkle with Romano cheese and bread crumbs.
Broil in preheated oven until just browned, about 5 minutes.