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.

Add ground beef to the skillet, cook until browned, breaking up the meat with a spoon.

Pour in white wine, cook for 10 minutes over medium heat until reduced.

Add diced tomatoes to the meat mixture, bring to a boil, then simmer for 15 minutes.

Meanwhile, prepare béchamel sauce: melt butter in a saucepan, whisk in flour, then gradually add milk, cook until thickened, season with salt and pepper.

Preheat oven to 400°F. Layer cooked noodles, meat sauce, béchamel sauce, and Parmesan in a baking dish. Repeat layers and finish with béchamel and cheese on top.

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