In the bowl of a stand mixer, add warm milk, yeast and sugar. Stir until combined.
Add eggs, melted butter and blue food coloring to the mixture and mix on low speed with a dough hook attachment for 2 minutes.
Slowly add flour one cup at a time until all flour is incorporated into the dough and pulled away from the sides of the bowl. The dough should be slightly sticky but not too wet or dry – if it is too wet, add more flour in 1 tablespoon increments; if it is too dry, add more warm milk 1 tablespoon at a time.
Knead for 5 minutes, then transfer to an oiled bowl, cover with plastic wrap or a damp cloth and let rise for 1-2 hours or until doubled in size.
Once the dough has doubled, punch it down and roll it out on a lightly floured surface into an 18×12-inch rectangle.
Spread the softened butter onto the rolled-out dough, then sprinkle with crushed Oreos, cinnamon and brown sugar. Starting at one end, tightly roll up the dough – like you would for a jelly roll cake – and pinch seams together to seal it. Slice into 12 equal pieces.
Grease an 8×8 inch baking pan with butter or cooking spray; then place rolls in the pan slightly apart from each other so they can rise during baking time. Cover with plastic wrap or a damp cloth and let rise again for 30 minutes to an hour until they have doubled in size.
Preheat oven to 375°F and bake cinnamon rolls for 25-30 minutes or until golden brown.
Prepare the icing by beating together softened butter, cream cheese and powdered sugar until creamy, then spread over warm cinnamon rolls right before serving.