Preheat your oven to 350°F (175°C) and prepare a square baking pan lined with parchment paper.

In a mixing bowl, combine gluten-free flour blend, baking powder, and salt. Whisk together.

In a larger bowl, cream together the unsalted butter, granulated sugar, and light brown sugar until fluffy. Mix in the egg replacer and vanilla extract.

Gradually combine the dry mixture with the butter mixture until just blended.

Spread the cookie dough evenly in the prepared baking pan and bake for 16-18 minutes until edges are golden.

For frosting, beat unsalted butter until smooth, then mix in powdered sugar and milk until fluffy.

Spread buttercream frosting over the cooled cookie base, slice, and serve.