Cook mince, onion, garlic, mushrooms for 10 minutes. Add tomatoes, wine, herbs, plus 1 tomato can of water. Simmer for 25 minutes, stirring occasionally. Season.
Heat oven to 200C/fan 180C/gas 6. Tip half mince into a baking dish. Add 3 sheets lasagne, then rest of mince and lasagne. Lay over tomatoes, spinach. Mix 3 tbsp milk with the cornflour. Pour rest of milk into a pan, stir in cornflour mix. Simmer, whisking until smooth. Season. Pour over the spinach. Sprinkle with Parmesan. Bake for 30 minutes.