In a large mixing bowl or the bowl of a stand mixer fitted with a paddle attachment, cream together the butter, sugar and brown sugar until creamy, approximately 1 minute.
Add the eggs, milk and vanilla, blending again until fully mixed.
In a separate bowl, sift together the flour, cornstarch, baking powder and salt. Add to wet ingredients in 2-2 incorporations. Blend until just mixed, do not overmix.
Fold in chocolate pieces by hand or with a few quick blends of an electric mixer.
Cover and refrigerate dough for 2-4 hours.
When ready to bake, preheat the oven to 375°F and line a baking sheet with parchment paper.
Portion dough into ½ cup balls, each will be about the size of a baseball. Using your palms, flatten into a hockey puck shape, leaving it about ½-3/4 inch thick. Place them 1-2 inches apart on a baking sheet.
Bake for approximately 15 minutes or until edges are starting to turn light brown. For a gooier cookie, remove at 14 minutes, for a more well baked cookie, remove at 16 minutes.
Allow to cool on the baking sheet for 4-5 minutes then using a spatula, remove to a wire cooling rack.
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Notes
For chocolate, either chop up baking chocolate, use jumbo chocolate chips (milk chocolate, not semi sweet) or I even just cut Hershey kisses in half.