Combine the flour, baking powder, baking soda and salt in a bowl. Set aside.
In the bowl of a stand mixer (or use a hand held) cream together the butter, brown sugar and powdered sugar until light and fluffy, about 2 minutes. Add the peanut butter and egg and beat until smooth and combined. Add the mashed banana and vanilla, beating until smooth.
Gradually beat in the flour mixture. Stir in the chocolate chips. Line two baking sheets with parchment paper or silpats.
When the oven is preheated drop about two teaspoons dough onto the prepared baking sheets.
Bake for 7 to 10 minutes and do not over cook. If anything undercook. Cool completely before filling.
To make the filling, place the egg whites, sugar, and cream of tartar in the heatproof bowl of an electric mixer (or if you do not have a stand mixer use a regular heat proof bowl). Set over a saucepan with simmering water. Whisk constantly until sugar is dissolved and whites are warm to the touch, 4 minutes.
Transfer the bowl to stand mixer fitted with the whisk attachment, and beat, starting on low speed, gradually increasing to high, until stiff, glossy peaks form, 5 to 7 minutes. Add vanilla, and mix until combined.
To fill the cookies flip half the cookies upside so the flat side is facing up. Spoon or pipe about 2 teaspoons of the marshmallow frosting onto all the cookies, leaving about 1/4 inch border. Wait 5 to 10 minutes and then top each cookie with it's other half. Line the cookies up in rows on a balking sheet and let the frosting set completely, about 1 hour. Try to tightly line the cookies up so that they are upright and strait. Some of my cookies wanted to slide to the side and I ended up with a few cookies that were crooked.
Store in an airtight container.
*Frosting from [Martha Stewart | http://www.marthastewart.com/314199/marshmallow-frosting]