In a large bowl, cream together butter and both sugars with a whisk. Whisk in egg and vanilla extract.
In a separate bowl, whisk flour, cornstartch, baking soda, and salt together. Add dry ingredients to the wet ingredient bowl, stirring together until well combined and dough has formed. It will be thick. Stir in white chocolate chips and cherries to evenly distribute.
Cover bowl with plastic wrap and let dough chill in fridge for at least 2 hours.
Remove cookie dough from fridge, let rest at room temperature until dough is more pliable and easier to roll (about 20-30 minutes). Preheat oven to 350 degrees while waiting. Line two baking sheets with parchment paper, set aside.
Scoop dough with a cookie scoop or a metal spoon and roll into a ball with your hands. Place about 12 cookies onto each baking sheet, about 2 inches apart.
Bake for 9-10 minutes. They will look a little undone, but do not over-bake, they will firm up as they cool down. Let cool for 5 minutes on baking sheet, then cool completely on a wire rack.
These stay fresh at room temperature (in an air-tight container) for 1 week.