Preheat the oven to 350°F. Line two baking sheets with parchment paper.
In a large mixing bowl, beat the butter, brown sugar, and granulated sugar until light and fluffy, about 2 to 3 minutes.
Beat in the eggs and egg yolk one at a time until fully incorporated.
Mix in the root beer extract and vanilla extract.
In a separate bowl, whisk together the flour, cornstarch, pudding mix, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients and mix just until combined.
Scoop the dough into 2-tablespoon portions and place on a parchment-lined tray.
Refrigerate the dough for 20 minutes.
Arrange the dough balls 2 inches apart on the prepared baking sheets.
Bake for 9 to 11 minutes, or until the edges are set and the centers still look slightly soft.
Cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.