1.Grease and line a regular loaf pan with parchment, making sure to leave an overhang for easy removal of the loaf. Add 2 tablespoons instant coffee to the hot water, stir, and allow it to cool.
2.In a large bowl, beat together 1/2 cup butter, 3/4 cup brown sugar and caster sugar until well combined. This will take about 2-3 minutes using an electric hand mixer.
3.Add in the eggs and vanilla and beat until well combined, light, fluffy, and smooth. About 2-3 minutes using an electric mixer. Pour in the cooled coffee mixture.
4.Preheat the oven to 355°F. In a separate bowl add, flour, salt, and baking powder. Whisk until combined. Pour into wet mixture and using a spatula mix to combine. Add walnuts and mix until well combined. Pour into the loaf tin.
5.Bake for 50-60 minutes or until a toothpick comes out mostly clean from the center of the loaf. Allow the cake to cool in the tin for 15 minutes before placing it on a cooling rack to cool completely.
6.Combine milk with the ½ teaspoon of instant coffee, stir, and set aside. In a large mixing bowl, combine the room-temperature cream cheese and 2 tablespoons butter. Beat with an electric hand mixer until smooth and combined. This will take about 3-5 minutes. Add in 3 tablespoons brown sugar and beat until well combined and dissolved. This will take about 3 to 5 minutes.
7.Add in the coffee milk and mix through. Then add 10 tablespoon of the powdered sugar and mix. Continue adding the sugar one tablespoon at a time until the frosting is a nice spreadable consistency. Spread the icing over the top of the cake. Slice and serve.