Heat olive oil in a large pot over medium-high heat. Add the onion, carrot, and celery and cook for 3-4 minutes until softened.
Add the ground beef and cook, breaking it up, until no pink remains. Stir in the garlic, nutmeg, salt, and pepper.
Add the red wine and simmer for 1-2 minutes. Stir in the marinara, milk, and water. Simmer for 12-15 minutes, stirring occasionally, until slightly thickened but still loose.
Meanwhile, make the bechamel: melt the butter in a saucepan over medium heat, whisk in the flour, and cook for 1 minute without browning. Gradually whisk in the milk and cook, whisking, until thickened, about 5 minutes. Season with salt, white pepper, and nutmeg.
Stir 1/3 cup of the bechamel into the ragu.
Lightly oil a 9x13 baking dish. Spread a thin layer of bechamel on the bottom, then add 3 no-boil noodles. Top with 1/3 of the ragu and a sprinkle of Parmesan. Repeat twice more.
Pour the remaining bechamel over the top and finish with a generous layer of Parmesan.
Cover with foil and bake at 400°F for 20 minutes. Uncover and bake another 5-8 minutes, or broil briefly, until golden and bubbling.
Let rest for 8-10 minutes before slicing and serving.