FOR the Cookie Base:
BEAT together the butter, sugar, and egg until creamy, then beat in the vanilla extract. In a separate bowl, whisk together the flour and baking powder then add into the butter mixture and beat on low until evenly combined with no dry pockets. Press this into an ungreased non-stick 15 x 10 jelly roll pan to cover the bottom of the pan. The cookie dough does not need to go up the sides of the pan (indeed, it'll slump down while baking even if you do try to work it up the sides.) Lightly cover with plastic wrap and place in the refrigerator for a half an hour.
PREHEAT the oven to 400°F.
BAKE the cookie base for 15 minutes, or until set up and golden brown. The edges may be slightly more brown, but should not be a deep brown. Let it cool completely in the pan before topping.
TO Make the Topping and Prepare the Tiramisu Bar Cookies:
STIR together the coffee or espresso and rum. Spoon 2 tablespoons of it into the bowl of a stand mixer or mixing bowl. Add the cream cheese, mascarpone, and vanilla extract and beat until smooth and creamy. Sift in the confectioner's sugar and beat until smooth and fluffy.
BRUSH the remaining coffee or espresso and rum mixture onto the cooled cookie base. Spread cream cheese mixture evenly over cookie base.
GRATE the chocolate bar with a fine grater over the cream topping.
CUT into 20 servings.