Wild mushroom lasagne with a parmesan cream

Name: Wild mushroom lasagne with a parmesan cream
Ingredients: 1 tbsp olive oil; 600g wild mushrooms; 50g unsalted butter plus extra knob for frying; 50g flour; 500ml milk; 2 egg yolks; 25g gruyère or vegetarian alternative, grated; 25g large sheets fresh cheddar or vegetarian alternative, grated; 3 3 large sheets fresh pasta (about 12 x 20cm), cooked; 200ml double cream; 100g butter; 50g parmesan or vegetarian alternative, grated; a little milk; 3 mixed peppers peeled, deseeded and thinly sliced; olive oil for frying