PREHEAT oven to 350°F.
CREAM together the butter and sugars in a stand mixer until smooth, about 2-3 minutes. Add the eggs and vanilla, making sure to scrape down the sides of the mixing bowl. Add the flour, salt, baking soda and baking powder and mix on low until everything is incorporated. Stir in the morsels by hand. Cover the dough with plastic wrap and refrigerate for at least 2 hours.
SCOOP heaping tablespoon (1 level cookie scoop) worth of dough and roll the dough into a ball. Place the cookies onto a parchment lined baking sheet, about 12 per sheet, and add a few morsels on the tops of the dough balls (these will allow the morsels to be front and center once baked). Bake for 12-14 minutes until the edges are just slightly golden brown and the center is still a bit soft.
REMOVE the baking sheet from the oven and let the cookies rest for about 10 minutes before transferring them to a cooling rack. Repeat this process for the remaining dough.
BEAT cream cheese, powdered sugar and vanilla extract in mixing bowl until creamy.
STACK 1 cookie on a small cake plate and add a dollop of frosting on top. Repeat so there are 3 layers to each cake and finish with a dollop of icing. Add morsels on top and serve as needed.