To make the bolognaise sauce, heat a large pan. Add the oil with the onion, carrot, celery, garlic and thyme. Cook for 8-10 minutes until the vegetables have softened and taken on a little colour, stirring occasionally. Add the minced beef and mix until well combined, then sauté until well browned, breaking up any lumps with a wooden spoon. Stir in the tomato puree and continue to cook for another minute or two, stirring.
Pour the tomatoes into the beef mixture and season to taste. Bring to the boil, then reduce the heat to the lowest setting and simmer for 1 hour until tender and the sauce has slightly reduced.
To make the cheese sauce, melt the butter in a pan. Stir in the flour and cook for 1 minute, stirring. Remove from the heat and gradually pour in the milk, whisking until smooth after each addition. Season to taste. Bring the sauce to the boil, whisking constantly, then reduce the heat and simmer gently for 5 minutes until smooth and thickened, stirring occasionally. Remove from the heat and stir in most of the Cheddar cheese until melted.
To cook the lasagne, preheat the oven to 180C (350F), Gas mark 4. Line 2 x 2.25 litre (4 pint) ovenproof dishes with a layer of lasagne sheets, breaking them to fit as necessary. Add half of the Bolognese and spread it into an even layer. Spread over half of the cheese sauce. Cover with another layer of the remaining lasagne sheets. Use the rest of the Bolognese to make another layer and then pour over the remaining cheese sauce. Scatter the rest of the Cheddar on top and bake for 1 hour or until the lasagnes are bubbling and lightly golden. Serve straight to the table with a plate of garlic bread and a bowl of salad.