Preheat your oven to 350°F. Grease a 9x13 inch baking pan.
In a large mixing bowl, combine the gluten-free yellow cake mix, melted butter, egg, and vanilla extract. Mix until well combined. It should be a bit crumbly.
Press the mixture into the bottom of the prepared pan to form a crust.
In another bowl, beat the softened cream cheese until smooth. Add the eggs, vanilla extract, and powdered sugar. Mix until smooth and combined.
Pour the cream cheese mixture over the crust, spreading it evenly.
Bake in the preheated oven for about 40-45 minutes or until the edges are golden brown and the center is set. If it becomes too brown, cover with aluminum foil.
Allow the cake to cool completely in the pan on a wire rack. For best results, refrigerate the cake for 1–2 hours before cutting, as this makes slicing cleaner and easier. Once chilled, cut the cake into squares and dust the top with powdered sugar. (You can also freeze the cake for about an hour before cutting for even cleaner slices.)