To prepare the shallots: Fill a deep saucepan with about 2 inches of vegetable oil. Heat over medium heat until a deep-fat thermometer reads 360 degrees. (Alternatively, use an electric deep-fat fryer). Toss the shallots with the flour in a large bowl, to coat. Transfer to a strainer and shake to remove the excess flour. Add the shallots to the hot oil and cook until golden brown, about 2 minutes. Remove the shallots with a slotted spoon, drain on paper towels, and sprinkle with salt and pepper.
Wash the spinach in several changes of cold water. Drain in a colander and pile into a large non-reactive pot. Place the pot over medium heat and cook, stirring, until just wilted, about 3 minutes. (The spinach will steam and cook in the water clinging to its leaves.) Drain and rinse under cold running water. Use your hands to squeeze out the water. Transfer to a work surface and coarsely chop. Melt the butter in a small saucepan over medium heat. Add the flour and cook, stirring, for 2 minutes. Pour in the milk, whisking constantly, and increase the heat to medium-high. Bring to a simmer, stirring often, and cook until thick and smooth, 3 to 5 minutes. Season with nutmeg, salt, and pepper. Stir in the spinach just before serving and warm through under low heat, about 3 minutes.
Serve the spinach hot, garnished with the fried shallots.
When I was making creamed spinach on the show, a fellow named John from Brooklyn called in to tell me his favorite way to squeeze water out of blanched spinach: in a potato ricer! I tried it, and he is right.