Preheat your oven to 375°F. Line rimmed baking sheets with unbleached parchment paper, and set them aside.
Prepare the chocolate.
Using a standard grater or very sharp knife, grate or finely chop the cold milk chocolate into a bowl.
Working with the chocolate when it’s cold makes it much easier to chop or grate it into pieces that don’t melt together.
Cover the bowl and place it in the refrigerator to chill until you are ready to add the chocolate to the cookie dough.
Prepare the dry ingredients.
In a medium-size bowl, place the flour, xanthan gum, oat flour, salt, baking powder and baking soda, and whisk to combine well.
In a separate, small bowl, place the chocolate chips and chopped nuts, and toss with 1 tablespoon of the dry ingredients.
Set both bowls aside.
Prepare the cookie dough.
In the bowl of a stand mixer fitted with the paddle attachment (or a large bowl with a handheld mixer), cream the butter on medium-high speed until it is light and fluffy.
Add the granulated sugar and brown sugar, and then the egg and vanilla and beat on medium-high speed until the mixture is smooth and light.
Add the dry ingredients and the milk, and mix on medium speed until just combined.
If the dough is very, very stiff, add more milk by the teaspoon until it can be stirred without too much difficulty.
Add the chocolate chips and nuts, and mix by hand until they are evenly distributed throughout the dough.
Remove the grated/chopped chocolate from the refrigerator, uncover it, and fold it carefully into the cookie dough, taking care not to melt it.
Shape the cookie dough.
Divide the dough into balls about 1 1/2-inches in diameter.
With the bottom of a glass, press down the balls of dough into disks, and place about 2 inches apart on the prepared baking sheets.
Bake the cookies.
One baking sheet at a time, place in the center of the preheated oven and bake until just set (8 to 10 minutes).
Remove from the oven and allow to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Notes
Adapted from this food.com recipe for the famous Neiman Marcus $250 cookies, which seems to be quite different from this actual Neiman Marcus recipe.