Add the softened butter and granulated sugar to a large mixing bowl. Beat with an electric mixer until light and fluffy.

Add the egg and vanilla extract. Beat until smooth and thoroughly combined.

Add the all-purpose flour, baking powder, and salt. Mix just until a soft cookie dough forms.

Divide the cookie dough into 2 equal portions.

On a lightly floured work surface, roll each portion of dough into a rectangle approximately 10 x 12 inches.

Make the cinnamon filling. In a small bowl, mix the softened butter, brown sugar, and cinnamon until thoroughly combined.

Divide the cinnamon filling evenly between the 2 rectangles. Spread the filling over each rectangle in an even layer.

Starting at one long side, tightly roll each rectangle into a log.

Wrap each cookie dough log tightly in plastic wrap.

Refrigerate for at least 1 hour, or until the dough is firm enough to slice cleanly.

Preheat the oven to 350°F. Line baking sheets with parchment paper.

Remove the chilled dough logs from the refrigerator and unwrap them.

Using a sharp knife, slice each log into ¼-inch-thick rounds.

Arrange the cookies on the prepared baking sheets, leaving approximately 2 inches between each cookie.

Bake for 10 to 12 minutes, or until the edges are just beginning to turn lightly golden.

Remove the cookies from the oven and let them cool on the baking sheets for 5 minutes.

Transfer the cookies to a wire cooling rack and allow them to cool completely.

Make the vanilla glaze. Add the powdered sugar, milk, and vanilla extract to a small bowl. Whisk until smooth.

Drizzle the vanilla glaze over the completely cooled cookies.

Allow the glaze to set before serving.