Lazy Bolognese-Style Lasagna

Salt and pepper
1 pound wavy lasagna noodles, broken into irregular pieces
2 tablespoons EVOO (extra-virgin olive oil)
1 1/2 pounds ground beef
1 onion, finely chopped
2 to 3 large cloves garlic, finely chopped
1 small carrot, finely chopped or grated
1 sprig rosemary, finely chopped
A sprinkle ground cloves
1/4 cup tomato paste
1 cup white wine
2 cups beef stock
3 tablespoons butter
2 rounded tablespoons flour
2 cups whole milk
Freshly grated nutmeg, to taste
Freshly grated parmigiano-reggiano cheese

Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente.
In a dutch oven, heat the EVOO, 2 turns of the pan, over medium-high heat. Add the beef and brown well. Add the onion, garlic, carrot, rosemary, cloves and lots of salt and pepper and cook until tender, 7 to 8 minutes. Stir in the tomato paste for 1 minute, then stir in the wine for 1 minute. Stir in the stock and simmer for a few minutes longer.
Preheat the broiler and position a rack in the center of the oven. In a saucepan, melt the butter over medium heat. Whisk in the flour, then the milk, and let thicken enough to coat a spoon; season with salt, pepper and nutmeg.
Toss the pasta with the meat sauce and arrange in a casserole. Pour the béchamel sauce over the top in an even layer. Top with a layer of parmigiano-reggiano and broil in the oven to brown the top.

recipe source: rachael ray