Heat the milk in the microwave for about 40 seconds until warm to the touch (around 110°F).
Pour the warm milk into the bowl of a stand mixer and sprinkle the yeast on top.
Add the sugar, egg, egg yolk, and melted butter. Whisk until well combined.
Stir in the flour and salt with a wooden spoon until a dough begins to form.
Knead the dough by hand on a floured surface for about 10 minutes, or use a dough hook in a mixer on medium speed for about 8 minutes.
If the dough is sticky, add 1–2 tablespoons of additional flour until a soft, slightly sticky dough ball forms.
Place the dough in an oiled bowl, cover with plastic wrap and a warm towel, and allow it to rise for 1–1½ hours until doubled in size.
On a lightly floured surface, roll the dough into a 14 x 9 inch rectangle.
Spread softened butter evenly over the dough.
In a bowl, mix brown sugar, cinnamon, black cocoa powder, and crushed Oreos. Sprinkle evenly over the buttered dough and gently press into the butter.
Roll the dough tightly into a log starting from the short side.
Trim uneven ends and cut the dough into 10 rolls using a serrated knife or dental floss.
Grease a 10-inch baking pan and line with parchment paper. Arrange the rolls inside.
Cover with plastic wrap and a warm towel and allow to rise for 30–45 minutes.
Preheat the oven to 350°F (175°C).
Bake for 25 minutes or until the edges are lightly golden. Avoid overbaking.
Let the rolls cool in the pan for 5 minutes.
To make the icing, beat milk, cream cheese, butter, powdered sugar, and vanilla until smooth and fluffy.
Spread icing over the warm Oreo Cinnamon Rolls and sprinkle with crushed Oreos before serving.