In a large mixing bowl, combine warm milk with active dry yeast, letting it sit until foamy. Mix in sugar, egg, egg yolk, melted butter, and vanilla extract. Gradually add flour and salt; knead until smooth, then add blue gel food coloring and let rise for 1–1½ hours.

Mix together softened butter, brown sugar, and ground cinnamon. Stir in crushed cookies and mini chocolate chips until well combined.

Roll out the dough into a rectangle. Spread the filling mixture over the dough, then roll tightly and slice into 12 equal rolls.

Place sliced rolls in a greased baking dish. Let them rise for another 30–45 minutes, then bake at 350°F for 20–25 minutes until golden brown.

Beat softened cream cheese and butter until smooth. Gradually add powdered sugar and vanilla extract, adding milk to achieve desired consistency.

Drizzle the cream cheese icing over the baked rolls, and sprinkle with crushed cookies and mini chocolate chips. Serve warm.