Line a baking sheet with parchment paper and set aside. In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and ground cinnamon until evenly combined.

In a large mixing bowl or stand mixer bowl, beat the softened butter, granulated sugar, and 1/4 cup light brown sugar on medium speed for 2–3 minutes, until light and fluffy. Scrape down the sides as needed.

Add the egg and 2 teaspoons vanilla extract to the creamed mixture and beat until smooth and creamy, about 30–45 seconds. Mix in the milk on low speed; the batter may look slightly curdled, which is fine.

Add the dry ingredient mixture to the bowl in two batches, mixing on low just until no streaks of flour remain. Stop as soon as the dough looks cohesive and, if needed, finish folding by hand with a spatula to avoid overmixing.

Turn the dough onto a large sheet of parchment paper and gently pat it into a rough rectangle. If very sticky, lightly flour the top or chill for 10 minutes. Place another sheet of parchment on top and roll into a 10 x 14-inch rectangle, about 1/4 inch thick. Slide the dough (still between parchment) onto a baking sheet and refrigerate for 15–20 minutes, until slightly firm.

In a small bowl, stir together the melted butter, 1/2 cup light brown sugar, 1 1/2 tablespoons cinnamon, 1 teaspoon vanilla, and a pinch of salt until it forms a thick, spreadable paste. If too runny, add a little more brown sugar; if too thick, add a bit more melted butter.

Remove the top parchment from the chilled dough. Spread the cinnamon sugar filling evenly over the surface, leaving about 1/4 inch bare around the edges, especially on the long edge farthest from you. Starting at the long edge closest to you, use the bottom parchment to help roll the dough tightly into a log. Gently pinch the seam closed and roll the log to even out the thickness. Wrap tightly in parchment, then in plastic wrap if available.

Chill the wrapped dough log in the refrigerator for at least 2 hours and up to 24 hours so it firms up and slices cleanly. For longer storage, freeze the log for up to 2 months and thaw in the fridge overnight before baking.

When ready to bake, preheat the oven to 350°F (175°C) and line a baking sheet with fresh parchment. Unwrap the chilled dough and slice into 1/4–1/3-inch thick rounds with a sharp or serrated knife, making straight-down cuts. If any spirals squish, gently reshape. Arrange cookies about 2 inches apart on the sheet and bake for 10–12 minutes, until edges are set and centers are puffed but still soft and only very lightly golden. Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.

In a small bowl, beat the softened cream cheese and 2 tablespoons softened butter until smooth and creamy. Add the powdered sugar, vanilla, and a pinch of salt. Mix on low, then add 1 tablespoon milk or cream. Add more liquid a teaspoon at a time as needed until the glaze is thick but pourable for drizzling.

Once cookies are completely cool, drizzle the cream cheese glaze over the tops with a spoon or piping bag in lines or zigzags. Let the glaze set for 15–20 minutes before serving.