Heat the oil in a large heavy-based pan over medium heat. Cook the onion and celery, stirring, until vegetables soften. Add minced beef, then cook, breaking up the lumps with a wooden spoon, until the beef changes colour.
Stir garlic and tomato paste into the beef mixture, then cook for 1 minute. Add canned tomatoes and carrot, then oregano and stock, stirring until mixture is well combined. Bring to the boil. Reduce heat, then simmer for 10 minutes or until thickened slightly.
Spread ½ cup white sauce over base of the dish. Top with a layer of pasta sheets, a third of the bolognese sauce, ½ cup parmesan and 1 cup white sauce. Repeat layering two more times, starting with pasta sheets and ending with the remaining white sauce.
Melt the butter in a medium saucepan over low heat, so it keeps its colour and doesn't brown. Sprinkle the flour over melted butter, then stir well with a wooden spoon until the butter is incorporated and the mixture forms a smooth paste (this is called a roux).
For the white sauce, pour in half the milk, whisking continuously, into the roux until liquid is completely incorporated and starts to thicken. Add remaining milk in a thin steady stream, whisking vigorously until mixture is smooth.
Bring the white sauce to the boil; boil thoroughly so the mixture thickens. Reduce the heat to low and cook the mixture for a few minutes, stirring occasionally, to cook out the raw taste of the flour. Leave to cook until ready to use.