Prepare Cookie Dough: In a medium bowl, whisk together the flour, cornstarch, baking powder, baking soda, and salt. Set this dry mixture aside.
In a large mixing bowl (or using a stand mixer), beat the softened butter and cream cheese together for about 2 minutes until it's light and fluffy.
Add the granulated sugar and continue to cream for another 2-3 minutes until the mixture is truly light and fluffy.
Beat in the egg and vanilla extract until everything is well combined.
Gradually add the dry flour mixture to the wet ingredients, mixing just until everything comes together. Be careful not to overmix the dough.
Chill the Dough: Divide the cookie dough into two equal portions. Shape each portion into a rough 6 to 8-inch square on a piece of plastic wrap. Wrap them tightly and chill in the refrigerator for about 2 hours. This step is key for easy rolling and shaping!
Get Ready to Bake: Around 10 minutes before your dough is done chilling, preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats.
Make the Filling: In a small bowl, combine the brown sugar and ground cinnamon using your fingers or a fork until well mixed.
Assemble the Rolls: Lightly flour a clean work surface. Take one chilled dough square from the fridge and place it on the floured surface. Dust the top with a little more flour, then roll it into a rectangle, roughly 12 inches wide by 10 inches deep. If any edges crack, simply pinch them back together.
Brush half of the melted butter over the dough, leaving a ½-inch strip unbuttered along the top edge (farthest from you). Quickly sprinkle half of the brown sugar-cinnamon mixture evenly over the buttered area, gently pressing it down to help it stick.
Roll and Slice: Lightly dampen the unbuttered edge of the dough with a little water using a pastry brush or your finger. This helps seal the roll. Starting from the side closest to you, tightly roll the dough towards the damp, unbuttered edge. Make sure it's snug, then press the seam to seal.
Using a sharp knife or even dental floss, slice the log into about 20 pieces, each about ½ inch thick.
Bake the Cookies: Place the sliced cookies onto your prepared baking sheets. Bake for about 10-12 minutes, or until the edges are just barely set. Let the cookies cool on the pan for 8-10 minutes before carefully transferring them to a wire rack to cool completely.
Repeat the rolling, slicing, and baking process with the second dough portion.
Whip Up the Icing: While the cookies cool, beat the softened cream cheese in a medium bowl until light and fluffy. Add the powdered sugar, milk, and vanilla extract, mixing until smooth and thick enough to drizzle. Add a tiny bit more milk if needed for desired consistency.
Finish and Serve: Once the cookies are completely cool, generously drizzle them with the cream cheese icing. Let the icing set for a bit before storing them in an airtight container. Enjoy!