Preheat the oven to 350 F (180 C) and line an 8x8 inch baking pan with parchment paper. In a separate bowl, sift together the flour, baking powder, and salt.
In a large bowl with a hand mixer, or in the bowl of a stand mixer with a whisk or paddle attachment, beat the butter, goat cheese, and maple sugar. Mix for 30-60 seconds, until the majority of the lumps are gone, although the goat cheese may remain a little lumpy.
Add the egg and mix for around 1 minute, scraping the sides of the bowl to make sure the batter is well combined.
Add half of the flour mixture and mix for about 30 seconds, until it is only just incorporated. Add the milk and mix for another 30 seconds, followed by the second half of the flour. Mix until just combined; do not overmix or the cake may become tough.
Bake at 350 F (180 C) for about 25 minutes, or until the cake is slightly browned on top and a toothpick or chopstick inserted into the center comes out clean. Allow the cake to cool for at least an hour before frosting.