Whisk the egg whites in a large clean bowl until stiff. Gradually whisk in the sugar, a teaspoonful at a time, until it has all been added. Whisk for a few minutes more until the meringue mixture is thick and glossy.
Fold in the pistachios then spoon heaped teaspoonfuls of the mixture into rough swirly mounds on 2 large baking sheets lined with nonstick baking paper.
Bake in a preheated oven, 110°C (225°F), Gas Mark ¼, for 45–60 minutes or until the meringues are firm and may be easily peeled off the paper. Leave to cool still on the paper.
Melt the chocolate in a heatproof bowl set over a saucepan of gently simmering water. Lift the meringues off the paper and dip the bases into the chocolate. Return to the paper, tilted on their sides and leave in a cool place until the chocolate has hardened.
To serve, whip the cream until just holding its shape then use to sandwich the meringues together in pairs. Arrange in paper cake cases, if liked, on a cake plate or stand. Eat on the day they are filled. (Left plain, the meringues will keep for 2–3 days.)