Preheat the oven to 170°C (340°F) and brush a 22cm (9 inch) loose bottom tart tin with melted butter.
Add the chopped chocolate to a heat-proof bowl set over a saucepan of simmering water. Melt gently and stir occasionally. Set aside to cool slightly.
To the bowl of an electric mixer fitted with a paddle attachment, add the sugar and butter. Beat at medium speed until the mixture is light in color and creamy.
Add the eggs to the butter and sugar mixture one at a time and beat well between each addition. Scrape down the sides of the bowl and mix again briefly.
Sift the flour and salt together in a separate bowl.
Add the dry ingredients to the egg mixture, beating at a low speed until just combined.
With the mixer running at medium-low speed add the milk and vanilla to the filling mixture and beat until just combined. Scrape down the sides of the bowl and beat again briefly.
With the mixer running at medium low speed add the melted chocolate in a steady stream to the pie filling. Use a spatula to scrape down the sides of the bowl and mix again, ensuring the brownie mixture is well combined.
Add the chopped walnuts to the chocolate fudge pie filling and fold them through using a spatula.
Pour the brownie batter into the prepared baking tin and bake in a preheated oven for 30 minutes or until the filling is set but not overcooked. Allow the pie to cool to room temperature.
