In a large pan, heat the olive oil over a low heat. Fry the onion, carrot and celery for 5 mins, or until softened. Add the mince and fry on a medium heat until golden. Stir in the tomato purée, chopped tomatoes and stock.
Meanwhile, make the white sauce. Melt the butter in a small saucepan over a low heat and add the flour. Whisk until combined and cook on low for 1-2 mins. Remove from the heat and gradually whisk in the milk until you have a loose sauce. Season. Return to a gentle heat and whisk constantly until the sauce thickens.
Preheat the oven to gas 6, 200°C, fan 180°C. Layer up the lasagne in a baking dish, starting with a third each of the ragu, then the pasta, then the white sauce. Repeat twice. Top with the cheese then bake in the oven for 40-45 mins, until piping hot and crisp and bubbling on top. Serve immediately.