In a large bowl, combine warm milk and active dry yeast. Let it sit for 5 minutes until frothy. Stir in granulated sugar, eggs, melted butter, and vanilla extract. Gradually add flour and salt to form a dough, knead until smooth, adding blue gel food coloring until desired hue is achieved. Let dough rise in a greased bowl for 1-1.5 hours until doubled in size.

While the dough rises, prepare the filling by blending softened butter, brown sugar, and ground cinnamon. Fold in crushed cookies and mini chocolate chips until combined.

Once risen, punch down the dough and roll it out on a floured surface into a rectangle. Spread the filling evenly, roll tightly into a log, and slice into 12 pieces using dental floss.

Place sliced rolls in a greased baking dish, cover with a towel and let rise for another 30-45 minutes. Preheat oven to 350°F. Bake for 20-25 minutes until golden.

In a bowl, beat together cream cheese and butter. Gradually add powdered sugar and vanilla extract, mixing until smooth. Adjust with milk for desired consistency.

Drizzle icing over warm rolls and top with crushed cookies and chocolate chips. Serve warm.