Line 2 baking sheets with parchment paper.
In a stand mixer or in a large bowl with a hand mixer, cream butter and both sugars on medium-high for 2-3 minutes, until mixture is light and fluffy.
Scrape down the sides of the bowl, add egg and peppermint extract, and beat for an additional 6 minutes.
Reduce mixer speed to low and add flour, baking powder, baking soda, and salt. Mix until just combined, taking care not to over-mix.
Mix in cornflake crunch, mini chocolate chips, and crushed candy canes/peppermints, until just combined. Fold in mini marshmallows.
Using about ⅓ cup of cookie dough, scoop out dough onto baking sheets about 4 inches apart. Try to push marshmallows into dough balls instead of leaving on outside as this will prevent spreading. Pat the tops of the cookie dough gently with your hand to flatten a bit. Refrigerate for at least 1 hour to chill dough.
When cookies are almost done chilling, pre-heat oven to 375 degrees.
Bake for 9-11 minutes, until the cookies are just beginning to brown. Cool completely on pan before enjoying or moving to an airtight container.