Heat the olive oil in a large Dutch oven or deep skillet over medium heat. Add the onion, carrot, and celery and cook for 7 to 9 minutes, stirring often, until softened. Add the garlic and cook for 30 seconds.

Add the ground beef, 1 teaspoon of the salt, and the pepper. Cook, breaking it into small crumbles, until no pink remains and the meat reaches 160°F (71°C). Spoon off excess fat if needed.

Stir in the tomato paste and cook for 1 minute. Add the crushed tomatoes, broth, oregano, and remaining 1/2 teaspoon salt. Simmer uncovered for 30 to 35 minutes, stirring occasionally, until thick enough that a spoon dragged across the pan leaves a brief trail.

Melt the butter in a medium saucepan over medium heat. Whisk in the flour and cook for 1 minute. Gradually whisk in the warm milk. Cook, whisking, for 6 to 8 minutes until the sauce coats the back of a spoon. Season with the salt and nutmeg.

Heat the oven to 375°F (190°C). Lightly grease a 9-by-13-inch baking dish. Spread a thin layer of meat sauce over the bottom.

Arrange 3 noodles over the sauce. Add one quarter of the remaining meat sauce, one quarter of the béchamel, and about one fifth of the mozzarella. Repeat to make four noodle layers, finishing with the remaining sauces, mozzarella, and all of the Parmesan.

Cover with foil greased on the underside so the cheese does not stick. Bake for 30 minutes.

Remove the foil and bake for 15 to 20 minutes more, until bubbling, browned in spots, and the center reaches 165°F (74°C).

Let the lasagne rest for 20 minutes. This is not decorative patience: the sauces settle and the pasta finishes absorbing moisture, so the slices hold together.

Cut into 8 portions and serve warm. Add a crisp salad or steamed greens if you want something fresh beside the rich layers.