Preheat oven to 350℉. Grease a 9x9-inch square pan with nonstick cooking spray or line it with parchment paper.
Prepare the Filling: Stir together sugar and cinnamon in a small bowl. Set aside.
Prepare the Topping: In another bowl, stir together gluten-free flour, sugar, and cinnamon. Stir in melted butter. Mix with a fork until crumbly. Set aside.
Prepare the Batter: Whisk together gluten-free flour, baking powder, baking soda, and salt in a small bowl. Set aside. In a large bowl, mix together butter, sugar, and eggs until smooth and creamy, about one minute.
Spread half the batter into the prepared pan. Sprinkle the cinnamon-sugar filling over the batter. Spread the remaining batter over the following. Top with cinnamon streusel topping.
Allow the cake to cool in the pan before serving. Store the cake covered on the counter for up to four days.
Gluten-Free Flour: Use a gluten-free flour blend that contains xanthan gum or whisk xanthan gum into the flour before using. For the streusel, whisk ⅛ teaspoon into the flour. For the batter, whisk ½ teaspoon of xanthan gum into the flour.