Heat olive oil over low heat in a large saucepan or deep frying pan.
Add the onion, carrots, celery and garlic. Cook slowly for about 8-10 minutes or until softened. Transfer to a bowl and set aside.
Turn up the heat and cook the mince in the same frying pan until browned.
Add the vegetables back into the pan with the cooked mince; stir in tomato puree, red wine, fresh and tinned tomatoes, bay leaves and thyme.
Let the sauce cook for 1 hour over low heat.
For the cheese sauce: Melt the butter in a heavy-based saucepan. Add the flour and cook for 1-2 minutes, stirring continuously. Gradually whisk in 300ml of milk, a little at a time, until you have a smooth sauce. Add the grated cheese, whisk again, then gently simmer for 5 minutes. Remove from the heat and set aside until ready to layer the lasagne.
Preheat oven to 180 degrees C. Bring a large pot of water to the boil and cook fresh pasta sheets for 1 or 2 minutes to soften.
To arrange the lasagne: cover the bottom of a large baking dish with lasagne sheets. Pour over a layer of bolognese sauce and spread to cover. Spoon the white sauce onto the bolognese layer, then cover with lasagne sheets. Repeat layers of bolognese, white sauce and fresh pasta sheets. Sprinkle over grated cheese.
Cook in the oven for 25-30 minutes, or until the cheese has melted and browned.