Rub the butter together with the flour and icing sugar by hand in a bowl or pulse in the food processor until fully combined.
Add the cold water and either pulse in the food processor, or mix through with a round knife until it comes together.
Knead the pastry a couple of times so it comes together in a smooth ball. Cover and put in the fridge to chill for 15 minutes.
Prepare The Pastry Case
Preheat the oven to 190C/375F (170C/340F fan assisted). Place a flat baking sheet on the middle shelf.
On a floured board, roll out the pastry and use it to line the pie/quiche tin, leaving some pastry overhanging.
Use a rolling pin to trim the edges away by simply rolling it over the top of the tin. If your tin has rounded edges, use a sharp knife instead.
Place the tin in the freezer for 10 minutes to harden.
Line the inside of the pastry case with baking paper and fill with baking beans.
Cook the pastry for 15 minutes, then remove the paper and cook for a further 10-15 minutes until the base of the pastry looks dry/sandy with no grey or wet looking patches.
Make the brownie filling
Reduce the oven to 180C/350F (160C/320F fan).
Put the butter and chopped dark chocolate in a large, heatproof bowl. Gently melt until smooth. You can use the microwave to do this, using 30 second bursts and stirring after each burst. Alternatively, you can put an inch of water in a pan, place the bowl on top (so that the water isn't touching the bowl) and bring to the boil so that the steam gently melts the chocolate, stirring as you go.
Whisk the sugar in. The mixture will thicken - graininess at this stage is fine.
If the mixture is hot, wait until it's just slightly warm before adding the beaten egg and vanilla. Whisk together until smooth.
Sift the flour into the bowl. Gently fold through until evenly combined.
Pour the filling into the pie case.
Bake for 35-40 minutes until set all the way across. A skewer pushed into the centre of should reveal sticky crumbs.
Place on a wire rack to cool to cool. While still warm, top with the chocolate chips. Leave to cool completely in the tin.
Chill overnight to firm up before slicing into wedges.