Preheat oven to 350°F (177°C). Line a cookie sheet with parchment paper.
Make the flax egg and set it aside.
Place the butter in a mixing bowl. Use either a handheld or stand mixer on medium speed and beat until light and fluffy. Add the sugars and beat again until light and fluffy. Finally, add the flax egg and vanilla and beat again to combine.
In a separate bowl, combine the flour, cornstarch (see note), baking soda, baking powder, and salt. Stir to combine. Pour the flour mixture in with the butter mixture. Stir to combine.
Add the chocolate chips and Teddy Gerahams, reserving some of each for topping each cookie. Be sure to cover the cookie dough when not in use to prevent it from drying out.
Drop by rounded spoonful about 2 inches apart on prepared cookie sheet. (Or you can roll the cookie dough balls for more precise edges to the cookies). Add additional chocolate chips to the top of each cookie and top with a Teddy Graham.
Bake cookies for 9 minutes (or up to 11 minutes, depending on your desired final cookie texture). If you prefer chewier cookies, remove them at 9 minutes. If you prefer crispier, cook for a few minutes longer. See note.
Once the cookies are done, allow them to cool for a minute or two on the cookie sheet before transferring to a wire rack to cool completely.
Make the entire batch of cookies or make a partial batch today and freeze the rest of the cookie dough to make more fresh cookies later.
Store in a sealed container for up to a week either on the counter or in the fridge. Or you can freeze these cookies for up to two months.