Preheat oven to 350 degrees.
Line 3 baking sheets with parchment paper and set aside.
In small bowl, combine flours, cocoa, baking soda, baking powder and salt. Set aside.
In a stand mixer, or bowl ready with hand mixer (these can also be done by hand with a wooden spoon or spatula, you will just need good muscles to do it). Attach paddles to stand mixer if using. Place softened butter and sugars into mixing bowl. Beat on medium speed until they are light and fluffy. Scrape down sides of bowl as needed.
Add eggs, milk, and vanilla. Mix again, this time only to combine. After the eggs are added it is easy to overmix, so be mindful of this. Scrape bowl as needed.
Next add in flour mixture. Mix only to combine. Scrape down and mix again if needed.
Add chocolate chips and mix for just a few seconds.
Scrape down bowl and remove beaters.
Scoop cookies to baking sheet. Leave a few inches of spacing, these do spread a little. I placed about 10-12 per baking sheet, if that gives you a better idea.
With the size of cookie I made, check the scoop link in the post, my cookies took right about 10 minutes. Let me say too though, I like a very soft and tender cookie. If you like a crispier cookie, you will want to bake another 3-5 minutes.
Remove cookies from oven. Allow to cool for a few minutes on the pan, then with a spatula transfer cookies to a cooling rack. Continue to allow to cool.
If you are topping with the crushed candy canes, prep them now. I unwrap and place them in a plastic bag. The bag then goes on my wooden cutting board and is smashed with a rolling pin. It won't take much to break them up to the size you want for the cookies.
Next, place about ¼ cup white chocolate chips in microwaveable bowl. Place in microwave on HIGH for about 15 seconds. Continue to microwave for 10 second increments, until you can see little areas of melted chocolate. Once you see small areas, start mixing. Mix it for about 20 seconds before returning to microwave if needed. Once it is smooth, drizzle over cookies. Before the chocolate sets, sprinkle with the crushed candy canes. How much chocolate and candy canes you use is a personal preference. Some like a lot , some just a hint. We are generally a mid range family, as shown in photos.
Now, sit back and enjoy. You deserve it!