DOUGH: Sprinkle yeast over warm water. Add about 1 teaspoon of sugar and stir to combine. Let sit for 5-7 minutes to allow mixture to bubble and activate.
In the bowl of a stand mixer, whisk together yeast mixture, warm milk, remaining sugar, egg, and egg yolk. Whisk salt into flour.
Add 2 cups of flour to mixing bowl. Use the dough hook attachment to mix together. Add another 1 cup of flour. Continue to knead on low speed while adding softened butter 1 Tbsp at a time. Add remaining cup of flour and knead until 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 dough has doubled in volume.
Punch down risen dough. Transfer to a clean working surface. Roll dough into a 20 x 14- inch rectangle.
FILLING: Spread softened butter over dough. Sprinkle sugar and chopped cookies on top. Gently press until dough.
Starting at the long side, roll dough into a log. Slice log into 12 equal parts. Place rolls into a greased 9 x 13-inch baking pan (quarter sheet pan size) . Cover with plastic wrap and let rest for 30-45 minutes at room temperature to allow roll to rise.
Preheat oven to 350°F. Remove plastic wrap and bake rolls for 30-33 minutes until golden brown on top and the internal temperature of the rolls hit 185° F. Allow rolls to rest for 5 minutes to slightly cool before frosting.
CREAM CHEESE FROSTING: Beat together cream cheese and butter until smooth. Add vanilla, salt, and powdered sugar. Beat until smooth. Spread over warm rolls. Top with chopped Oreo cookies.