Line a baking sheet with parchment paper or silicone baking mats. Also line a small baking sheet, 9x13, or cutting board with parchment paper and set aside.
In the bowl of a mixer whip the softened butter until it starts to pale in color. Add in the brown sugar and mix until combined. Add the eggs, oil, and vanilla to the butter mixture and whip on medium high speed until light and fluffy (3-4 minutes).
In a separate bowl, mix the flour, cornstarch, baking powder, and salt together.
When the butter mixture has become light and fluffy, slowly add in the flour mixture about 1 cup at a time. Mix until all is combined.
Scoop ¼ cup of the dough into your hands then roll it into a ball. Place the ¼ cup dough ball onto the small parchment lined baking sheet, it is OK for the dough balls to be touching, as you will not be baking them quite yet. Continue to do this until all of the dough has been formed into balls.
Place the tray of dough into the refrigerator for 15-20 minutes. While the dough is chilling, preheat the oven to 350 degrees.
After 15 minutes, remove 6 of the balls of dough. Place them onto the full sized baking sheet evenly, leaving plenty of space between each one. Use the bottom of a measuring cup or drinking glass to press each dough ball down to be approximately ½ - ¾ inch thick.
Bake the cookies in the preheated oven for 10-12 minutes. The cookies should still be very blonde in color, no golden edges. Remove from the oven and let cool completely.
Repeat steps 7 and 8 until all of the cookies have been baked.
While the cookies are chilling, you can make the buttercream.
In a stand mixer with a paddle attachment, add the softened butter. Whip the butter until it becomes smooth and lighter in color. Add the brown sugar, powdered sugar, vanilla, and salt. Whip on medium high until it begins to fluff up. Reduce the speed to medium and while the mixer is running slowly drizzle the heavy cream in. Give the buttercream a final good mix on medium high speed until everything is combined, and light and fluffy.
Transfer the buttercream to a piping bag with an open round tip, or no tip. Pipe the buttercream onto the chilled cookies starting in the center then spiraling your way to the edges. Then use the back of a spoon to smooth the buttercream out on each cookie, giving them flat tops.
Sprinkle the top of each cookie with mini semi-sweet chocolate chips and small pieces of edible cookie dough.
Cookies are best served chilled. Store in a single layer in an airtight container, keep refrigerated.