Line 2 large baking sheets with parchment paper; set aside.
In a medium bowl, combine the 1 1/2 cups chocolate chips and 1 cup mini chocolate chips; set aside.
In a large, microwave safe bowl, melt 1/2 cup butter. Let cool to room temperature, at least 10 minutes.
When the butter is cool, whisk in the 1 cup brown sugar until smooth. Add 1 egg and 1 teaspoon vanilla to the bowl and stir until completely smooth. Stir in 1/2 teaspoon baking soda, 1/2 teaspoon baking powder, 1/2 teaspoon cornstarch and 1/2 teaspoon salt.
Stir in the cake flour, followed by the all-purpose flour. Be careful no to overmix the dough. Fold in 1 3/4 cups of the chocolate chip mixture.
Use a 1/2 cup measurer to divide the dough into 5-6 equal portions. Shape each portion into a ball and place on the prepared baking sheets, 3 inches apart. Press the remaining chocolate chips onto the top and sides of the cookie dough balls, flattening the cookies as you press to about 1 1/2 inch thickness. Don't press chocolate chips on the bottom of the cookie--they will burn.
Place the baking sheets in the refrigerator for one hour. If you don't have room for the cookie sheets in your refrigerator, place the cookies on a plate and transfer to the baking sheets after chilling. While the cookies chill, preheat the oven to 325 degrees.
Bake for 15-20 minutes, or until cookies are just set in the middle. For soft cookies, do not overbake. Allow the cookies to cool on the baking sheets for 5 minutes, then transfer to wire racks to cool completely.