In a medium saucepan, melt 4 tablespoons of butter over medium heat. Stir in ¼ cup of flour to form a roux, cooking for about 2 minutes until golden. Gradually whisk in 3 cups of warm whole milk, reducing heat to low. Simmer for 15-20 minutes, stirring continuously until thickened. Season with salt, pepper, and a pinch of nutmeg; set aside to cool slightly.

In a large skillet, heat 2 tablespoons of olive oil over medium heat. Add finely chopped onion, diced carrot, and celery, sautéing for about 5-7 minutes until soft. Incorporate 1 pound of ground meat, cooking until browned. Stir in a tablespoon of tomato paste and a can of crushed tomatoes, then pour in ½ cup of red wine. Let it simmer gently for at least 30 minutes to meld flavors, stirring occasionally.

Preheat your oven to 375°F (190°C). In a large baking dish, spread a thin layer of Béchamel sauce on the bottom. Begin layering with lasagna sheets, followed by a layer of Ragù, more Béchamel, and a sprinkle of grated Parmigiano. Repeat layers until all ingredients are used, finishing with Béchamel and Parmigiano on top.

Place the assembled lasagna in the preheated oven. Bake uncovered for 35-40 minutes, until the top is golden and bubbly. For an extra crunch, switch to broil for the final 3-4 minutes, watching closely to avoid burning.