Cook zucchini and peas in a pan of salted simmering water for two minutes only,then drain,cool under cold running water and drain again. Heat oven to 190C.
Beat eggs with milk,cheese,salt and pepper. Heat one tablespoon of butter in a large oven-proof frypan. Add egg mixture and cook for one minute,then add sweet potato,zucchini and peas,jiggling the pan so they settle into the egg.
Cook over moderate heat for five minutes,drawing back the edges to tip the runny egg into the pan to help it cook.
Transfer pan to the oven and bake frittata for 15 minutes or longer,until just set. Trim mushrooms and cut each into three thick slices. Heat remaining butter and olive oil in a pan and cook mushrooms until browned,about 10 minutes.
Toss with chopped parsley,sea salt and pepper and serve with big wedges of frittata.
Serve warm from the oven with roasted mushrooms,or if someone needs a meat fix,with pan-fried chorizo.