Preheat the oven to 350°.
In the bowl of a stand mixer cream together the butter and sugar until light and fluffy.
Scrape the sides of the bowl and add the eggs, vanilla and oil. Mix until combined.
Lastly, add in the flour and baking powder. Mix until the dough forms. The dough will be soft.
Scoop your dough out into generous 1/3 cup portions. Roll the cookie dough into a ball and then flatten the cookie dough slightly. Repeat with the remaining dough, arrange on pan and set aside.
In a small bowl, combine the brown sugar, cinnamon and melted butter with a fork.
Once the mixture is combined, press about 1/2 tbsp of the mixture onto the top of each cookie.
Bake at 350° for 9-11 minutes. The cookies will spread and just start to crackle when you take them out of the oven. They should not turn brown. Allow the cookies to cool on the pan.
While the cookies are cooling, make the cream cheese frosting.
Make the frosting by combining the butter and cream cheese, mixing until completely smooth.
Add in the powdered sugar 1/2 cup at a time, allowing the powdered sugar to mix into the cream cheese mixture before adding more powdered sugar.
Once all of the powdered sugar has been added, add the vanilla.
Add a splash of milk or heavy cream if needed to achieve your desired thickness.
Transfer the frosting into a piping bag fit with a large round piping tip (1D) or into a large zip top bag with the corner clipped.
Pipe a swirl on the top of the warm cookies, allowing space in between the swirl to see the brown sugar layer.
Serve warm.