Preheat oven to 375 degrees. Line two baking sheets with parchment paper.
In the bowl of a stand mixer, beat the butter and sugar until fluffy. Beat in the eggs and vanilla. (Alternatively, do this part in a large bowl using an electric hand mixer.)
In a separate bowl, whisk together the flour, baking powder and salt.
With the mixer running on low speed, slowly add the dry ingredients until combined.
Using a 3 Tbsp. cookie scoop, scoop cookie dough balls and place them 1 inch apart onto the baking sheets. Flatten each dough ball with a spatula. Using a wooden or metal skewer, make criss-cross depressions into each cookie in a waffle pattern.
Bake 23-25 minutes. Cool on the cookie sheet for 5 minutes before removing onto a wire rack.
Make the frosting: Combine the butter, sugar, vanilla and milk in a stand mixer and beat until smooth. Using a 1 Tbsp. cookie scoop, place one scoop of frosting onto each cooled cookie. Drizzle with maple syrup.