Line two large baking sheets with parchment paper and set aside. Also, line a large cutting board with parchment paper and set it aside.
In a large bowl or stand mixer fitter with a paddle attachment, whip the softened butter until it starts to pale in color. Scrape down the sides and add in the brown sugar and mix until combined.
1 cup salted butter, 2 cups light brown sugar
Add the eggs, oil, and vanilla to the butter mixture and beat at medium-high speed until light and fluffy, about 3 to 4 minutes.
2 large eggs, ½ cup canola or vegetable oil, 1 Tablespoon vanilla extract
Meanwhile, in a separate bowl, whisk together the flour, cornstarch, baking powder, and salt together.
4 cups all-purpose flour, 2 teaspoons cornstarch, 1½ teaspoons baking powder, ¾ teaspoon salt
When the butter mixture is light and fluffy, slowly add in the flour mixture about 1 cup at a time. Mix until all is combined.
Use a 1/4 cup measuring cup to scoop ¼ cup of the dough into your hands, then roll it into a ball. Place the ball of dough onto the small parchment-lined baking sheet, it is okay for the dough balls to be touching, as you will not be baking them quite yet. Repeat until all of the dough has been formed into balls.
Place the tray of dough into the refrigerator for 15 minutes. While the dough is chilling, preheat the oven to 350°F.
After 15 minutes, remove 6 of the balls of dough. Place them onto the full-sized baking sheet at least 4 inches apart. 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 to 12 minutes. The cookies should still be very blonde in color with no golden edges. Allow them to cool for a couple of minutes on the baking sheet before transferring them to a wire tack to cool completely, about 30 minutes.
Repeat steps 7 and 8 until all of the cookies have been baked. Rotating baking sheets as you go so you don't put dough down on a hot sheet.
While the cookies are cooling, prepare the buttercream in a stand mixer with a paddle attachment. Whip the butter until it becomes smooth and lighter in color.
¾ cup salted butter
Add the powdered sugar, brown sugar, vanilla extract, and salt. Whip at medium-high until it begins to fluff up. Reduce 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. About 1 minute.
1¾ cups powdered sugar, ¾ cup light brown sugar, 2 teaspoons vanilla extract, ¼ teaspoon salt, ⅓ cup heavy cream
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 small pieces of edible cookie dough and mini semi-sweet chocolate chips.
1 (8oz.) bag frozen edible chocolate chip cookie dough chunks, ½ cup semi-sweet mini chocolate chips
These cookies are best served chilled. Store in a single layer in an airtight container, keep refrigerated.