Preheat the oven to 200C/400F/Gas 6
Heat a large frying pan over a medium heat and add the olive oil. Once hot, add the mince along with a good pinch of salt and pepper. Brown the mince for 5-6 minutes until coloured all over and beginning to crisp. Remove the mince from the pan and set to one side.
Add the onion and carrot to the frying pan along with a pinch of salt. Cook gently for 10 minutes, or until everything is softened.
Meanwhile, melt the butter in a saucepan over a medium heat. Once melted, add the flour and mustard, stir to mix well. Leave to cook over a medium heat for two minutes, or until the mixture makes a paste.
Pour the milk in batches into the saucepan, whisking as you add to create a smooth white sauce. Once all the milk is added season with a pinch of salt and black pepper, turn the heat down and leave to simmer very gently for seven minutes.
Once the onions and carrots are softened, add the garlic to the frying pan and cook for two minutes. Return the meat (plus any juices) to the pan and add the tomatoes. Mix everything together, cover with a lid and simmer the sauce for 10 minutes until thickened slightly.
To assemble the lasagne, place a quarter of the tomato sauce into the bottom of a small/medium baking dish. Top with a layer of lasagne sheets. Spoon over another quarter of the tomato sauce and top with a third of the white sauce. Repeat this twice more, finishing at the top with the last layer of white sauce. (You should have three sets of layers of lasagne, tomato and white sauce, all on a bed of tomato sauce.)
Place into the preheated oven and bake for 30 minutes or until bubbling and the top is golden-brown. Serve the lasagne in slices while hot.