01 - Heat olive oil in a large skillet over medium heat. Add onion, carrot, and celery; sauté for 6 to 8 minutes until softened. Add garlic and cook 1 minute. Add ground beef and cook, breaking up meat, until browned. Stir in tomato paste and cook 2 minutes. Pour in wine and simmer until mostly evaporated. Add crushed tomatoes, oregano, basil, salt, pepper, and sugar if using. Simmer uncovered 30 to 40 minutes, stirring occasionally, until thickened.
02 - Melt butter in a saucepan over medium heat. Add flour and whisk for 1 to 2 minutes. Gradually whisk in warm milk; cook, whisking constantly, until thickened and smooth, about 6 to 8 minutes. Season with nutmeg, salt, and white pepper. Remove from heat.
03 - Preheat oven to 350°F. Spread a thin layer of ragù on the bottom of a 9x13-inch baking dish. Add a layer of lasagne sheets, then spread ¼ of the ragù followed by ¼ of the béchamel. Repeat layers three more times, finishing with béchamel. Sprinkle mozzarella and Parmesan evenly over the top.
04 - Cover loosely with foil and bake 30 minutes. Remove foil and bake an additional 15 to 20 minutes until golden and bubbling.
05 - Let lasagne rest 15 minutes before slicing and serving to allow layers to set.