Place the chocolate digestives in a plastic bag and crush with a rolling pin, then transfer to a large bowl. Place the butter in a small, heavy-based saucepan and heat gently until just melted, then stir it into the biscuit crumbs until well mixed. Press into the bottom and up the sides of a 23cm tart tin or dish.
To make the filling, place the egg yolks, caster sugar and cornflour into a large bowl and beat until they form a smooth paste, adding a little of the milk, if necessary. Place the milk in a small sauce-pan and heat gently until almost boiling, then slowly pour it into the egg mixture, whisking well.
Return the mixture to the pan and cook gently, whisking until thick. Remove from the heat. Whisk in the melted chocolate, then pour onto the biscuit base.
To make the meringue, whisk the egg whites in a large spotlessly clean bowl until soft peaks form. Gradually whisk in two-thirds of the sugar until the mixture is stiff and glossy. Fold in the remaining sugar and vanilla essence.
Spread the meringue over the filling, swirling the surface with the back of a spoon to give it an attractive finish. Bake in the centre of a preheated oven at 160C/375F for 30min or until golden. This chocolate merginue pie is best served warm or hot.