Preheat the oven to 350 degrees F.
In a large mixing bowl, combine the brown sugar, sugar, and butter, mixing until creamy.
Add in the egg and vanilla.
Once combined, mix in the flour and cocoa powder, scraping the sides of the bowl to make sure it is well combined. Using a large spoon or spatula, stir in the chocolate chips, evenly distributing them throughout the dough.
Once the dough is done, use a small portion scoop, or spoon, and place small portions, about 2 inches in size, onto the cookie sheet, with a little room in between each portion so cookies have room to spread.
Bake for 12-15 minutes. Remove from the oven and let the cookies cool.
Melt the white chocolate in the microwave, and drizzle over the cookies.
Top with crushed candy canes.