350g/12oz carrots, peeled and sliced into thin batons
1 tbsp chopped fresh parsley
850g/1lb 14oz potatoes (such as Maris Piper, Rooster or King Edward), peeled
4 banana shallots, thinly sliced lengthways
salt and pepper
450ml/16fl oz vegetable stock
butter, for greasing and frying
300ml/陆 pint double cream
75驳/2陆辞锄 Parmesan (or a similar vegetarian hard cheese), grated