Prep oven and pans. Position rack to center of oven and preheat oven to 350oF. Place cupcake liners into muffin pans and set aside.
Combine dry ingredients. In a large mixing bowl, whisk together flour, baking powder, and salt.
Cream butter and sugar. In the bowl of your stand mixer fitted with a paddle attachment, or in a mixing bowl with a hand mixer, cream the butter and sugar together on medium speed for about 2 to 3 minutes until light and fluffy.
Add eggs and vanilla. Add in the egg and egg white, and beat to combine. Scrape down the bowl as needed. Add in the vanilla and mix to combine.
Alternate dry ingredients and buttermilk. Add flour mixture and buttermilk alternately, beginning and ending with the flour mixture to the butter mixture and beat to combine. (I add 1/3 of the flour, then 1/2 of the buttermilk, then 1/3 of the flour, then rest of buttermilk, and then finish with the remaining flour.) Stop mixing once the flour has been incorporated. Do not overmix. Stir in crushed cookies with a spatula. Do not mix too much here or your batter will turn gray.
Bake cupcakes. Fill cupcake liners to ⅔ full. Bake for 18-20 minutes or until a toothpick comes out clean and the top of a cupcake springs back to the touch. Remove from the oven and let cool in the pan for 5 minutes. Transfer cupcakes to a cooling rack and cool completely.
Make the frosting. In a bowl of your stand mixer, with paddle attachment, beat the butter on medium-high speed for about 2 minutes to soften. Add the confectioners sugar ½ cup at a time, with mixer on low, and beat to combine. Scraping down the bowl as needed.
Add the heavy cream, vanilla, and salt. Beat to combine on low speed, then increase the speed to medium-high speed and beat for 7-8 minutes until light and fluffy.
Add the cookies. Fold in the crushed cookies with a spatula until evenly distributed. Frost cooled cupcakes, or refrigerate covered until ready to use.