Prepare the Dough: In a small bowl, sprinkle yeast over warm water. Add about 1 teaspoon of sugar and stir to combine. Let sit for 5-7 minutes to allow the mixture to bubble and activate.
In the bowl of a stand mixer, whisk together the yeast mixture, warm milk, remaining sugar, egg, and egg yolk. Whisk salt into flour separately.
Add 2 cups of flour to the mixing bowl. Use the dough hook attachment to mix together. Gradually add another 1 cup of flour and continue to knead on low speed while adding softened butter 1 tablespoon at a time.
Add the remaining cup of flour and knead until the dough is smooth and cleans the sides of the bowl. Add chopped cookies and mix until evenly distributed.
Transfer dough to a lightly greased bowl. Cover with plastic wrap and let sit at room temperature for about an hour until the dough has doubled in volume.
Once risen, punch down the dough and transfer it to a clean working surface. Roll the dough into a 20 x 14-inch rectangle.
Prepare the Filling:
7. Spread softened butter over the rolled-out dough. Sprinkle sugar and chopped cookies on top. Gently press the filling into the dough.
8. Starting at the long side, roll the dough into a log. Slice the log into 12 equal parts. Place the rolls into a greased 9 x 13-inch baking pan. Cover with plastic wrap and let rest for 30-45 minutes at room temperature to allow the rolls to rise.
9. Preheat the oven to 350°F. Remove the plastic wrap and bake the rolls for 30-33 minutes until golden brown on top and the internal temperature of the rolls reaches 185°F. Allow the rolls to rest for 5 minutes before frosting.
Prepare the Cream Cheese Frosting:
10. In a bowl, beat together cream cheese and butter until smooth. Add vanilla, salt, and powdered sugar. Beat until smooth. Spread the frosting over the warm rolls and top with chopped Oreo cookies.