Make the Dough: In a large bowl, cream together 1 cup softened butter and granulated sugar until light and fluffy. Beat in the egg and 2 teaspoons vanilla extract.
Combine Dry Ingredients: In a separate bowl, whisk together flour, baking powder, and salt. Gradually add to the wet ingredients, mixing until just combined. Do not overmix.
First Chill: Divide the dough in half. Flatten each half into a rectangle, wrap in plastic, and chill for at least 30 minutes.
Prepare Swirl: While dough chills, mix ½ cup softened butter, brown sugar, and cinnamon in a small bowl until a smooth paste forms.
Roll and Spread: On a lightly floured surface, roll one half of the dough into a 9×12-inch rectangle. Spread half of the cinnamon mixture evenly over it, leaving a small border.
Form Log: Roll the dough tightly into a log starting from the long side. Repeat with the second half of dough.
Second Chill: Wrap logs in plastic and chill for 1-2 hours until firm.
Bake: Preheat oven to 375°F (190°C). Slice logs into ½-inch thick rounds. Place on parchment-lined baking sheets. Bake for 8-11 minutes until edges are golden. Cool completely.
Glaze: Beat cream cheese and 2 tablespoons butter until smooth. Add powdered sugar, milk, and ½ teaspoon vanilla. Drizzle over cooled cookies.