While the red sauce is simmering, place a medium-size pot over medium heat and melt the butter. Sprinkle the flour over the melted butter and cook the mixture for about 1 minute. Whisk the milk slowly into the butter-flour mixture and cook until thickened. Season the white sauce with salt, freshly ground pepper and the nutmeg.
Cover two loaf pans with a layer of foil for easy removal from the pan. Ladle about 1 cup of the red sauce into the bottom of the first lined loaf pan. Put down a layer of lasagna noodles, then top them with about a cup of white sauce and a handful of Parmigiano Reggiano (about 1/4 cup). Continue building the lasagna, alternating layers of noodle, red sauce, noodle, white sauce and cheese, until all the noodles are covered. End the lasagna on a layer of red sauce and top it off with the grated provolone and some Parmigiano-Reggiano. Repeat this process with the other loaf pan and the remaining sauce.
Cover the pans with aluminum foil and bake for 30 minutes. Remove the foil and bake another 15 minutes until the noodles are tender and the cheese is melted and golden brown.
Remove the pans from the oven and let cool for 15-20 minutes to let the lasagna set. Pull the lasagna out of the pans by the edges of the foil, pull the foil down from around the lasagna and cut with a serrated knife. Garnish each slice with fresh parsley.