Heat olive oil in a large skillet over medium heat.

Add sliced carrots and chopped onions; cook for 3 minutes, then add minced garlic and cook for 1 minute.

Stir in ground beef and cook until browned, breaking it apart with a spoon.

Pour in white wine and simmer for 10 minutes.

Add diced tomatoes, bring to a boil, then reduce to simmer for 15 minutes.

Meanwhile, prepare béchamel sauce by melting butter, whisking in flour, then gradually adding milk, seasoning with salt and pepper, and simmering until thickened.

Preheat oven to 400°F. Cook lasagna noodles al dente. Butter a baking dish and spread a layer of béchamel on the bottom.

Layer noodles, meat sauce, béchamel, and sprinkle with Parmesan; repeat until all ingredients are used, ending with béchamel on top.

Bake uncovered for 35-45 minutes until bubbly and golden. Rest for 15 minutes before serving.