Preheat oven to 350°F and line two baking sheets with parchment paper.
In a large bowl, beat butter and sugar for 2-3 minutes until creamy and light, scraping the bowl as needed.
Add eggs and vanilla extract, mixing until fully combined.
Combine flour, cornstarch, baking soda, and salt; stir into wet ingredients on medium-low speed until just blended with a few flour streaks.
Fold in white chocolate chips and Lucky Charms cereal pieces along with marshmallows gently to distribute evenly.
Drop dough balls using a medium cookie scoop onto prepared sheets spacing a few inches apart.
Bake for 10-12 minutes until edges are set.
Press extra marshmallows onto the warm cookies immediately after baking.
Allow cookies to set on baking sheets for 5-10 minutes before transferring to a wire rack to cool completely.