Preheat the oven to 350°F and line a large baking sheet with parchment paper.
In a mixing bowl, beat the butter, brown sugar and cane sugar with a hand mixer until light and fluffy. Beat until well combined, about 4–6 minutes. The mixture will look like damp sand and hold together when pinched
Add the eggs and vanilla and beat again until smooth.
Add the flour, cornstarch, baking soda and salt. Mix on medium speed until the flour is incorporated. Use a rubber spatula to ensure all flour is mixed. Dough will be crumbly until a rubber spatula presses it together.
Fold in the chopped candy with a rubber spatula.
Use a medium cookie scoop (heaping 1.5 tbsp) to portion the dough onto the baking sheet. Recipe makes 24 cookies so 12 on each sheet. Gently press a few extra candy pieces into the top of each one.
Bake on the middle rack for 11-13 minutes, until the edges are golden brown. Be careful not to overbake. Note: middles may look slightly underdone and they will slightly spread in the oven. They will continue to bake as they cool.
Cookie-scooting trick. After removing the cookies from the oven, they will have lost their shape. Swirl a small glass bowl (or round cookie cutter/glass) around each cookie to shape it into a perfect circle. Give the swirl a shake while doing so to get bakery style cookies and better form.
Visually, here is what the cookies will look like when you remove from the oven vs. after cookie-scooting.
Let the cookies cool on the baking sheet for 5 minutes before transferring the parchment paper with all the cookies to a wire rack, allowing them to cool until centers firm. Repeat baking instructions for the second batch of cookies. Optional: press extra candy into the tops while they're still warm.