Cook the lasagna sheets a for 8-10 minutes. Drain the sheets and lie flat on towels to cool, then stack between sheets of parchment paper until ready to use. Set aside. Skip this step if using fresh pasta sheets.
To a saucepan add the butter over medium heat. When melted, whisk in the flour and cook for a few minutes until it turns a light golden color. Slowly pour in the milk while whisking. Bring to a simmer until thickened. Turn off the heat and stir in the nutmeg and a little salt to taste. Set aside.
Preheat oven to 375°F/190°C.
Set all your ingredients up in a line, Bolognese sauce, lasagna sheets, Parmesan cheese and the béchamel (white sauce).
Use unsalted butter to grease a 9 x 13-inch (23 x 33cm) casserole dish. Spread a ladle full of Bolognese sauce over the bottom of the pan in an even layer. Divide the ingredients into 5, you will be making 5 layers. Line with lasagna sheets on top of the sauce, slightly overlapping. Spread 1/5 of the Bolognese, sprinkle Parmesan cheese then drizzle a thin layer of béchamel sauce, you don't need to cover the entire area. Repeat, pasta, Bolognese, Parmesan, béchamel until all the ingredients are gone and the pan is full. The last topping being a layer of pasta with Bolognese and béchamel, top with Parmesan. See note for directions to prepare ahead.
Cover with foil, place on a baking sheet in case it bubbles over and bake for 30 minutes.
After 30 minutes remove the foil and bake for 15 minutes more. Use a small knife to insert into the pasta, it should be tender. If not, place back into the oven until done (cooking times will vary according to your oven and may be quicker if using fresh pasta).
Allow to rest for 30 minutes before slicing.