In a large mixing bowl, combine the flour, granulated sugar, yeast, and salt. Mix well.
In a separate bowl, whisk together the warmed milk, melted butter, egg, and vanilla extract.
Pour the wet ingredients into the dry ingredients and mix until a dough forms. Knead the dough on a floured surface for about 5 minutes until smooth.
Place the dough in a greased bowl, cover with a kitchen towel, and let it rise in a warm place for about 1 hour or until doubled in size.
Preheat your oven to 350°F (175°C).
Once the dough has risen, roll it out into a rectangle about 1/4 inch thick. Spread the softened butter over the dough.
In a small bowl, mix the crushed Oreo cookies, ground cinnamon, and brown sugar. Sprinkle this mixture evenly over the buttered dough.
Roll the dough tightly from one end to the other, then slice it into 12 equal pieces.
Place the rolls in a greased baking dish and let them rise for another 30 minutes.
Bake in the preheated oven for 20-25 minutes or until golden brown.
While the rolls are baking, prepare the frosting by mixing the powdered sugar, cream cheese, milk, and vanilla extract until smooth.
Once the rolls are done, let them cool for a few minutes before drizzling the frosting over the top.