In the bowl of a stand mixer fitted with the paddle attachment, or using a hand mixer and a large bowl, cream the butter with both sugars on medium-high speed until light and fluffy, 3 to 5 minutes. Reduce the speed to low and beat in the eggs, vanilla extract and peppermint extract until just combined. On low speed, gradually add the dry ingredients and beat until just incorporated. Add the chocolate chunks and mini marshmallows and beat on low until just combined. Cover the bowl and refrigerate for at least 1 hour or overnight.