Pre-heat oven to 180 deg C (350 deg F). Lightly grease and line the base of an 8-inch (20.5 cm) square baking pan or tin with greaseproof or baking paper.
Break up the 60 g plain chocolate and put it in a heatproof bowl. Fill a saucepan to about an inch (2 cm) deep with water, and bring to a gentle simmer over low heat. Set the bowl over the saucepan (making sure it sits above the water), and melt the chocolate gently, stirring frequently. Remove the bowl from the pan and set aside to cool until needed.
In an electric mixer bowl, put the soft butter and icing sugar. With an electric mixer fitted with a paddle attachment, beat at medium speed (speed 3 on my Kitchen Aid mixer) until light and creamy. Alternatively, you may beat by hand with a long wooden spoon.
Gradually beat in the eggs, followed by the rum. Scrape down the sides of the bowl, then add the melted chocolate and beat till well combined. Stir in the flour, and when thoroughly combined, add the chopped chocolate (or chocolate chips) and the walnuts and mix thoroughly. Pour out the batter into the prepared tin and spread evenly.
Bake in the pre-heated oven for about 20 to 25 minutes until the top is set and firm. Remove from the oven and place on a cooling rack, and leave to cool in the tin - taking care as the crust is fragile - before cutting into squares or bars. Serve warm or at room temperature.
Once cool, store in an air-tight container for up to 4 days.