In the bowl of a stand mixer (or a large mixing bowl), combine the warm milk (ensure it's not too hot, 105-115°F / 40-46°C), active dry yeast, and granulated sugar. Stir gently and let it sit for 5-10 minutes until foamy, indicating the yeast is active.

Add the salt, egg, and melted butter to the yeast mixture. Mix well.

Gradually add the all-purpose flour, about a cup at a time, mixing on low speed with the dough hook (or by hand) until a shaggy dough forms. Increase speed to medium-low and knead for 5-7 minutes until the dough is smooth, elastic, and pulls away from the sides of the bowl. If kneading by hand, knead on a lightly floured surface for 8-10 minutes.

Lightly grease a large bowl. Transfer the dough to the bowl, turning once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1 to 1.5 hours, or until doubled in size.

While the dough is rising, prepare the filling: In a small bowl, cream together the softened unsalted butter, light brown sugar, and ground cinnamon until well combined. Stir in the crushed chocolate chip cookies.

Once the dough has doubled, gently punch it down to release the air. Transfer the dough to a lightly floured surface and roll it into a large rectangle, approximately 12x18 inches.

Spread the filling evenly over the entire surface of the dough, leaving a small border (about 1/2 inch) on one of the long edges clean.

Starting from the long edge opposite the clean border, carefully roll the dough into a tight log. Pinch the seam closed to seal.

Using a sharp knife or unflavored dental floss, slice the log into 12 equal rolls, about 1.5 inches thick each.

Lightly grease a 9x13 inch baking dish. Arrange the sliced rolls in the prepared dish, leaving a little space between each.

Cover the baking dish loosely with plastic wrap or a clean kitchen towel and let the rolls rise again in a warm place for another 30-45 minutes, or until puffy and almost doubled.

Preheat your oven to 375°F (190°C) about 15 minutes before the second rise is complete.

Bake the cinnamon rolls for 20-25 minutes, or until golden brown on top and cooked through. If they start to brown too quickly, you can loosely cover them with foil.

Remove from the oven and let them cool in the pan for about 10-15 minutes before frosting.

While the rolls are cooling, prepare the frosting: In a medium bowl, beat together the softened cream cheese and softened unsalted butter with an electric mixer until smooth and creamy.

Gradually add the sifted powdered sugar, vanilla extract, and blue gel food coloring. Beat on low speed until combined, then increase to medium-high and beat until light and fluffy. If the frosting is too thick, add milk 1 tablespoon at a time until desired consistency is reached.

Spread the blue frosting generously over the warm cinnamon rolls. While the frosting is still wet, sprinkle with mini chocolate chip cookies and chocolate chips.

Serve warm and enjoy your delightful Cookie Monster Cinnamon Rolls!