In a large mixing bowl, cream together the softened butter and granulated sugar with an electric mixer until light and fluffy (2-3 minutes). Beat in the egg and vanilla extract until well combined. In a separate medium bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Stir in the milk until a soft dough forms. Do not overmix. Set aside.

In a medium mixing bowl, beat the softened cream cheese, granulated sugar, and vanilla extract with an electric mixer until smooth and creamy. Beat in the all-purpose flour until fully incorporated. Transfer the filling to a piping bag fitted with a small round tip or a Ziploc bag with a corner snipped off.

In a small bowl, combine the melted butter, packed light brown sugar, and ground cinnamon. Stir until a thick paste forms. Transfer to a separate small piping bag or Ziploc bag with a tiny corner snipped off.

Preheat oven to 350°F (175°C). Line two baking sheets with parchment paper. Scoop about 1.5 tablespoons of cookie dough for each cookie and flatten slightly into a disc on the prepared baking sheet.

Pipe a small dollop (about 1 tsp) of cheesecake filling onto the center of each flattened cookie dough disc. Then, pipe a small spiral or zigzag of the cinnamon swirl mixture over the cheesecake filling. Using a toothpick, gently swirl the cinnamon mixture into the cheesecake and slightly into the cookie dough to create a marbled effect. Be careful not to mix too much, just enough to swirl.

Bake for 10-12 minutes, or until the edges are lightly golden and the centers are just set. The cheesecake filling might still look slightly soft in the middle. Remove from oven and let cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.

While cookies cool, whisk together the powdered sugar, milk, and vanilla extract in a small bowl until smooth and desired drizzling consistency is reached. Add more milk a tiny bit at a time if too thick, or more powdered sugar if too thin. Transfer the glaze to a small piping bag or Ziploc bag with a very tiny corner snipped off.

Once the cookies are completely cool, drizzle the vanilla glaze generously over each cookie. Let the glaze set for about 15-20 minutes before serving.