Preheat the oven to 180°C.
Peel the vegetables and cut them into chunks. Put them into a pan of lightly salted cold water over a high heat then simmer until cooked through.
Meanwhile grease an oven dish and lay fish in it. Pour over the milk and put the dish in the oven for 20 minutes.
Drain the vegetables and mash them with a potato masher, mixing in the butter. Season with salt &pepper.
Take the fish out of the oven. Turn the oven up to 200°C or to the grill.
Scatter half of the peas and parsley over the fish. Mix the remaining peas with the mash, then spread it evenly over the fish, covering well.
Grate the cheese all over the mash, season with ground pepper, then return to the oven until golden brown - about 15 minutes.