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Heat oil in a medium sized heavy based saucepan over medium heat. Add onion, carrot, celery and garlic and sauté until softened.
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Add both types of mince, breaking up with a wooden spoon, and fry until browned.
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Add milk, tinned tomato, bay leaves and 500ml water and bring to the boil.
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Season with salt and pepper, lower heat and simmer for 1.5 hours, stirring occasionally.
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Preheat oven to 180C.
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Place a ladle of meat sauce in the base of a lasagna tray and place 2 lasagna sheets on top, trimming if necessary.
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Place 2 ladles of sauce on top and sprinkle with mozzarella and Parmesan.
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Repeat layers three more times, finishing with meat sauce topped with mozzarella and Parmesan.
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Cover the lasagna with aluminium foil and place in the oven for 30 minutes.
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Increase oven temperature to 200C, remove foil and bake for a further 15 minutes.
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Allow lasagna to rest for 15 minutes before portioning and serving.