Preheat oven to 400 degrees F (200 degrees C). Grease a baking sheet.
Whisk flour, sugar, and baking powder together in a large bowl. Cut cold butter pieces into flour mixture until it resembles coarse crumbs. Fold cream cheese into butter mixture.
Stir a small amount of the 3/4 cup milk into cream cheese mixture, continuing to add milk until the dough is sticky. Turn the dough out onto a work surface and knead until the dough is soft, 1 to 5 minutes.
Roll or cut dough into desired shape and arrange on the prepared baking sheet. Brush 1 tablespoon milk over the top of the dough.
Bake shortbread in the preheated oven until golden brown and fragrant, 15 to 25 minutes.