Preheat your oven to 350°F (175°C) and line a large baking sheet with parchment paper.
In a large bowl, beat the softened butter and 3/4 cup granulated sugar together until light and fluffy, about 3 minutes.
Add the egg and ube extract to the butter mixture, beating until well combined and vibrant purple.
Whisk the flour, baking powder, and salt together in a separate bowl, then gradually add this dry mixture to the wet ingredients, mixing until a soft dough forms.
Chill the dough for 30 minutes in the refrigerator to make it easier to handle.
Scoop about 1 tablespoon of dough at a time and roll it into a ball between your palms.
Roll each ball thoroughly in the 1/2 cup of powdered sugar until completely coated, then place on the prepared baking sheet spaced 2 inches apart.
Bake for 10 to 12 minutes, or until the edges are set and the tops have cracked; the centers should still look slightly soft.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
While the cookies cool, beat the cream cheese, 1/4 cup powdered sugar, and vanilla extract until smooth.
Once the cookies are fully cooled, spread a small dollop of the cream cheese filling onto the flat side of one cookie and press another cookie on top to form a sandwich.