Preheat oven to 350° F. Grease an 8 x 8-inch square pan and line it with a square of parchment paper.
In a large bowl using an electric mixer on medium speed, cream the ½ cup unsalted butter and 1 cup 1 ¼ cups brown sugar, divided until it is light and fluffy, about 2-3 minutes. Add the 2 large eggs and the 2 teaspoons pure vanilla extract, beating well to combine.
In a medium bowl, whisk together the 1 ¾ cups gluten free flour, 1 ½ teaspoon baking powder, and ¼ teaspoon fine sea salt. Add this mixture to the creamed mixture, alternating with the ½ cup whole milk.
Spoon the batter into the cake pan, and smooth the top with a spatula. Sprinkle the ¼ cup of additional brown sugar and the 1 teaspoon ground cinnamon evenly across the top. Rest for 20 minutes, then bake for about 30-35 minutes, until a tester inserted in the cake comes out clean. Remove from oven and cool in pan for 20 minutes. Turn out onto a rack to cool or cut and serve the cake directly from the pan.
Notes
Other flours. You can use a blend of oat and almond flour if you like (do 1 ½ cups (180 grams) of oat flour to ¼ cup (30 grams) of almond flour, or use a gluten-free flour blend of your choice.
Make it dairy-free. Substitute non-dairy butter and non-dairy milk for the butter and milk.
Coconut sugar. I love the dark, caramel note of coconut sugar, and it's lovely in this cake! You can swap all of the brown sugar for coconut sugar, or just use it in the topping.
Serve from the pan. I love the casual feel of this cake, and you can keep things even more easy by slicing and serving straight from the pan.
Adjust the size of the slices. I like generous portions, so I cut my cake into 9 slices. You can certainly cut them smaller if you wish!
Try a different pan. Feel free to bake the batter in an 8 or 9-inch cake round for a different presentation.