Preheat oven to 350°F (175°C). Grease a 9-inch round pan and line the bottom with parchment paper.
Brown your butter: melt in a pan over medium heat, stir until golden and nutty-smelling. Let cool 10 minutes.
In a large bowl, mix brown butter, brown sugar, and granulated sugar until smooth.
Stir in the egg, egg yolk, and vanilla until glossy.
Whisk together gluten-free flour, almond flour, baking powder, and salt. Add to wet ingredients and stir just until combined.
Fold in chocolate chips (crush half for better spread).
Spread dough evenly into the prepared pan. Press flat.
Bake for 30–35 minutes, until edges are golden and center is set. Toothpick should come out with a few moist crumbs.
Cool completely in the pan before frosting or slicing.
For frosting, beat butter until smooth. Add powdered sugar, cocoa, vanilla, salt, and milk. Beat until fluffy, adding more milk if needed.
Frost cooled cookie cake as desired. Pipe edges or drizzle with melted chocolate. Add sprinkles for decoration.