Preheat oven to 350 F and prepare your cookie sheets with parchment paper.
In a large bowl, cream butter and sugars until light and fluffy.
Add each egg one and a time mixing after each one to make sure incorporated. Then add vanilla and mix.
In a separate bowl whisk together the flour through to the salt.
On low, mix the dry ingredients to the wet in additions until fully mixed. Dough will be super thick.
Fold in chocolate chips.
Using a small cookie scoop, place balls of dough on cookie sheets and bake for about 9-12 minutes being careful to not overbake.
For the frosting, In a large bowl beat butter, dulce de leche, vanilla and sugar until fluffy.
Add milk to thin out frosting if needed.
Once cooled, pipe the dulce de leche frosting and top with another cookie.
Eat like the cookie monster. Try it. It's totally fun.