Preheat the oven to 350°F/180°c. Grease an 8 1/2 inch x 4 1/2 inch baking tin, or line the tin with parchment paper. Set aside.

Add the softened butter and granulated sugar to the bowl of a stand mixer. Beat on a high speed using a flat beater attachment for 3 minutes, or until pale and creamy.

Add the eggs and vanilla extract to the stand mixer and beat on a medium speed until well combined, scraping the sides of the bowl as necessary.

Add the flour, baking powder and salt, and beat on a low speed until just combined. Add the milk, and beat once again on a low speed and smooth and combined. Stir through 1 1/4 cups of the chocolate chips.

Pour the cake batter into the prepared baking tin. Bake for 1 hour, or until cooked through.

Allow to cool in the tin for 10 minutes before turning out onto a wire cooling rack to cool completely.

To make the chocolate frosting, add the powdered sugar, cocoa powder, softened butter, vanilla extract and salt to a mixing bowl. Add 2 tablespoons of boiling water to begin with, and mix with a mixing spoon until well combined. Add extra water, a little at a time, until the frosting has reached a spreadable consistency.

Spread the frosting evenly over the cooled cake and top with the remaining chocolate chips.