Preheat your oven to 350°F (175°C). Grease and flour a cake pan.
In a mixing bowl, cream the butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition.
In another bowl, whisk together the gluten-free flour, baking powder, and salt.
Gradually add the dry ingredients to the butter mixture, alternating with the milk. Begin and end with the dry ingredients. Stir in the vanilla extract.
Pour the batter into the prepared cake pan and smooth the top.
Bake for 30 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.