Place about half of the spinach and any water clinging to their leaves in a large saucepan. Cover and cook over medium-high heat, stirring often, until the spinach wilts, about 5 minutes. Stir in the remaining spinach and cook until all of the spinach is wilted and tender, about 5 minutes more. Drain in a colander and rinse under cold water.
A handful at a time, squeeze the excess water from the spinach and set the spinach aside.
Melt the butter in a medium saucepan over medium-low heat. Whisk in the flour and let bubble without browning for 1 minute. Whisk in the half-and-half and bring to a simmer over medium heat. Cook just until lightly thickened and no raw flour flavor remains, about 3 minutes. Stir in the spinach and nutmeg and cook until the spinach is heated through, about 3 minutes. Stir in the cheese. Season with salt and pepper. Serve hot.