Roast vegetable lasagne

Name: Roast vegetable lasagne
Ingredients: 3 carrots, peeled and finely chopped; 3 courgettes, finely chopped; 1 fennel bulb, trimmed and finely chopped; 2 sweet red peppers, finely chopped; 2 red onions, finely chopped; 2 tbsp olive oil; 600ml/20fl oz full-fat milk; 50g/1¾oz butter; 60g/2¼oz plain flour; large grating fresh nutmeg; 12 fresh or dried 18x13cm/7x5in lasagne sheets; butter, for greasing; 100g/3½oz Parmesan (or similar vegetarian hard cheese), finely grated; 250g/9oz mozzarella, well drained and chopped into small pieces; salt and freshly ground black pepper