In a medium-sized bowl, mix together packed brown sugar, cocoa powder, nutmeg, and ground cinnamon and set aside.
Dough:
Preheat oven to 200 degrees F.
In a large bowl or the bowl of a stand mixer, add 3 1/2 cups of flour, instant dry yeast, and salt.
In a separate bowl, add the milk, softened butter, and granulated sugar into a microwave-safe bowl.
Heat on high power for 60-90 seconds, until the mixture is warm. Stir to combine.
Gradually, with the mixer on medium speed and fitted with the dough hook, add the warm milk mixture into the flour mixture and mix until the dough comes together.
Add in the egg and mix at low speed until a sticky dough ball is formed. Mix on a medium-low speed for 2-3 minutes, until the dough becomes elastic.
Add additional flour, 1 tablespoon at a time until the dough begins to pull from the sides of the bowl.
Once you're done adding the additional flour, mix in 1/2 cup of the crushed Oreos. Mix until incorporated evenly throughout the dough.
Cover the bowl with plastic wrap, and set it aside to allow the dough to rest for 10-15 minutes.
Roll:
Flour the counter and roll the dough into a large rectangle 12 inches x 18 inches.
Spread 1/4 cup of softened butter evenly over the dough, leaving 1/2 inch on the long side of the rectangle uncovered.
Sprinkle the cinnamon roll filling evenly over the buttered area, and sprinkle the 1/2 cup of remaining crushed Oreos on top.
Tightly roll the dough toward the uncovered strip. After that, slice the log into 9 equal pieces.
Arrange them in a greased 8x8 inches square pan.
At this point, TURN OFF the oven. Cover the pan with foil and place in the oven for 30 minutes, or until the rolls have risen.
Remove the pan from the oven and take off the foil.
Turn the oven back on, and heat it to 350 degrees F.
Once preheated, bake the rolls for 26-30 minutes or until the rolls are golden brown.
Vanilla Cinnamon Roll Glaze:
Add unsalted butter to a medium-sized bowl with 1 1/2 cups of powdered sugar, 2 tablespoons of whole milk, and 1 teaspoon vanilla extract. Mix together until smooth.
Let the cinnamon rolls cool for 5-10 minutes, then drizzle the glaze over the still warm cinnamon rolls.