Preheat oven to 350°F. Line a cookie sheet with parchment paper.
In a large bowl, add in the butter, brown sugar, and granulated sugar. Using a hand mixer, beat on medium until light and fluffy.
Add in the eggs and vanilla extract. Beat until eggs are incorporated. Scrape down the sides of the bowl and mix in any remaining egg.
In a separate bowl, add in the flour, cocoa powder, baking soda, and salt. Whisk to combine.
Add the flour mixture into the wet ingredients and beat until the flour is just worked in.
Stir in 1 1/2 cups of the white chocolate peppermint chips.
Using a 1 1/2 tablespoon cookie scoop, scoop the cookie dough and place it about 2 inches apart on the prepared cookie sheet.
Break 1 to 2 pieces of the remaining peppermint chunks in half and push them into the top of the cookie dough. Leave some of the chip peeking out of the dough.
Place in the preheated oven and bake for 10 minutes. Let cool for 5 to 10 minutes on the cookie sheet and then transfer to a wire rack to cool completely.
Store in an airtight container.