To make the sauce: Place olive oil, onion and carrot into a large heavy based saucepan and sauté on medium heat for 5 minutes until onion begins turn translucent. Then add garlic and sauté another 5 minutes.
Add mince and break up into chunks, but don't pulverise it, keep the mince quite chunky. Sauté until the mince browns and caramelises. It's ok if it begins to stick on the pan.
Add wine and stir, picking up all the caramelised bits that may be stuck to the pan using your wooden spoon. Once bubbling has subsided, add napoletana sauce or passata and stir.
Reduce to the lowest heat and simmer for at least an hour, until the oil rises to the top. See the picture above.
When sauce is nearly finished, preheat oven to 180C fan-forced.
To make béchamel: In a small saucepan, add olive oil and flour on medium heat. Mix together with a spoon until it begins to simmer, this will cook the flour.
Then add 1/4 cup of milk at a time, and use a whisk to combine. Continue whisking while heating, the béchamel will begin to thicken. When the béchamel has a consistency of pancake batter, add another 1/4 cup of milk and whisk again.
Repeat this step until all milk is added. Then add nutmeg, parmesan and salt and whisk to thicken one last time to resemble thin pancake batter. Remove from heat and set aside, the béchamel will continue to thicken slightly.
To assemble: Use a ladle to spoon some meat sauce onto the bottom of an oven proof baking dish. Layer dry lasagne sheets without overlapping. Ladle more sauce spreading out evenly over the lasagne sheets, then add another layer of them. Repeat this until sauce is finished, making sure to add béchamel to the middle and final top layers.
Sprinkle or place cheese evenly on top of final béchamel and sauce layer.
Bake for 30-40 minutes, until the cheese is golden.
Rest for 10 minutes, then slice and serve.