Put the flour, milk, egg and salt and pepper in a blender or food processor and blend until smooth, or whisk with a fork in a bowl.
Heat a few drops of the oil in a nonstick frying pan. Pour in a ladleful of the batter and cook for 1 minute. Carefully flip the pancake over and cook the other side. Slide the pancake out of the pan on to greaseproof paper. Make 3 more pancakes in the same way, adding a few more drops of oil to the pan between each one, and stack the pancakes between sheets of greaseproof paper.
Meanwhile, make the filling. Put all the ingredients in a saucepan and cook for 5 minutes, stirring occasionally.
Divide the filling between the pancakes, reserving a little of the mixture to serve, then roll them up.
Transfer to an ovenproof dish and bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 20 minutes. Serve with the reheated reserved mushroom mixture, garnished with parsley sprigs.