In a medium pot over medium heat, melt butter.
Once melted, add flour and whisk until smooth, about 2 minutes.
Gradually pour in warm milk, whisking constantly to prevent lumps.
Season with salt, nutmeg, and black pepper.
Simmer and whisk until the sauce thickens and coats the back of a spoon, about 5-8 minutes.
Remove from heat, adjust seasoning, and set aside.
Preheat oven to 375º F. Line a large baking sheet with aluminum foil.
Butter a 13 x 9-inch baking dish.
Spread 1/2 cup of béchamel sauce on the bottom.
Arrange 3 pasta sheets side by side.
Evenly layer with bolognese sauce, then 1 1/2 cups béchamel sauce, and sprinkle with 1/2 cup Parmesan cheese.
Finish with a final layer of pasta sheets topped with remaining béchamel, Parmesan cheese, and mozzarella.
Cover dish with foil and place on baking sheet.
Bake on the middle rack for 45-50 minutes, until bubbling and pasta is tender.
Remove foil and bake uncovered for 15 minutes or until cheese is golden.
Let lasagna rest for 8-10 minutes before serving.