Preheat oven to 350°F.
In a medium bowl, sift together flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer, cream together butter and sugars on medium speed for at least 2 minutes, scraping down the sides as needed.
Add the egg, vanilla, and milk, and blend until smooth and fluffy, (about 30 seconds).
Add the flour mixture and mix on low until fully incorporated.
Chill the batter for 10-15 minutes.
Scoop ½ teaspoon-sized dollops of the batter (about 1 inch apart) onto a baking sheet lined with parchment.
Bake about 15 minutes, rotating halfway through baking (cookies will be golden brown)
Set aside to cool.
Lay the cooled vanilla wafers, flat side down, on a parchment-lined baking sheet.
Evenly distribute the banana simple syrup over the cookies. Set aside for 10 minutes.