Preheat oven to 350 and line 2 cookie sheets with parchment paper
In the bowl of an electric mixer with the paddle attachment cream butter and both sugars. Add the egg and vanilla and beat. In a separate bowl mix together flour, cocoa, soda, baking powder, salt. Then add to the butter and egg mixture. Mix just until blended. Drop 1 1/2 - 2 inch spoonfuls onto the parchment paper lined cookie sheets. Round them and flatten them a bit with your hand. Bake for 8-10 minutes until soft in the middle but firm around the edges. Remove from oven and let cool on the baking sheet for a few minutes before removing them to a wire rack to cool completely.
Take the ice cream out to soften a bit.
When completely cool turn a cookie upside down. Put a scope of ice cream in the middle. Cover with another cookie and flatten together. Wrap the sandwich with saran wrap and freeze immediately.
Makes 20 - 4 inch cookies for 10 ice cream sandwiches