In a large bowl, beat the butter and granulated sugar with a mixer on medium speed for 2 minutes, until light and fluffy. Beat in the milk and vanilla, then add the flour, baking powder and salt and mix on low until a soft dough forms.
Place the dough between two large sheets of parchment paper and roll it into a 10x12 inch rectangle, about 1/4 inch thick. Slide it onto a baking sheet and chill for 20 minutes, until firm but still flexible.
In a small bowl, stir together the softened butter, brown sugar and cinnamon until it forms a smooth, spreadable paste.
Peel off the top sheet of parchment and spread the filling evenly over the dough, leaving a 1/2 inch border along one long side. Starting from the opposite long side, roll the dough up tightly into a log, using the bottom parchment to help lift it.If the dough cracks, let it sit at room temperature for 5 minutes and try again.
Wrap the log tightly in plastic wrap and chill for 2 hours, or freeze for 45 minutes, until firm enough to slice cleanly.
Preheat the oven to 350°F and line two baking sheets with parchment paper. Slice the log into 1/3 inch rounds and place them 2 inches apart on the prepared sheets.
Bake for 10-12 minutes, until the edges are lightly golden. Cool on the sheet for 5 minutes, then transfer to a wire rack to cool completely.
Whisk the cream cheese until smooth, then whisk in the powdered sugar, milk and vanilla. Drizzle the glaze over the cooled cookies and let it set for 20 minutes. Makes about 32 cookies.