To prepare a thin mint cookie cake recipe, first you need to prepare the cake batter. First, you will need 2 cups of flour, 1 cup of baking powder, and 1 teaspoon of salt. Mix the dry ingredients with the wet ingredients until they are well combined. Then, add the butter and mix until it is light and fluffy. Add the vanilla and beat the mixture with an electric mixer for 2 minutes. Pour the batter into the prepared cake pan and bake for 35 to 40 minutes, or until the toothpick inserted in the center comes out clean. Allow the cakes to cool for 10 to 15 minutes before removing them from the pan.