In a large bowl combine flour, sugar, salt and yeast. Add warm (not hot) milk. Mix till well combined. Cover with cling film or a napkin and leave in a warm spot till it has doubled in volume, about 1 hour.
Divide dought in two equal parts. Roll out into flat rounds.
For the filling, saute onion in oil until almost transparent. Add sliced mushrooms and saute on high heat so the mushrooms release their liquid, about 5 minutes. Let cool.
Preheat oven to 200 C / Gas 6.
Roll out each piece of dough to a 20 cm circle and place on a baking tray lined with greaseproof paper, or on a baking stone.
Spread each pizza with 2 tablespoons pesto sauce. Top with mushrooms and onions. Sprinkle with feta and mozzarella. Season with ground black pepper to taste.
Bake till bubbly and the edges are browned, about 15 minutes.