Pre-heat oven to 350 degrees F.
Line your sheet pan with parchment paper and set aside.
In the large bowl of a stand mixer, cream together softened butter and sugar. Start at the lowest speed and increase as needed. Add in the egg and vanilla and continue to beat with the mixer to incorporate.
In a separate bowl, combine flour, cornstarch, baking soda, and salt. Mix well. Add flour mixture to the larger bowl slowly while you continue to beat on low.
Once your dough is mixed, fold in chocolate chips.
Press your dough (on the parchment paper-lined baking pan) into an even layer and bake on the center rack for 14-16 minutes, rotating the pan 180 degrees at the halfway mark for even browning/cooking.
Once your sheet pan cookies are baked, let cool for a few minutes and then start pressing out cookies with cookie cutters
To make the icing, add all the ingredients together and mix until creamy.