Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, sugar, baking powder, and salt in a food processor; pulse 3 times or until combined. Add chilled butter, cream cheese, and cider vinegar; pulse 4 times. Add ice water through food chute, 1 tablespoon at a time, pulsing just until combined (do not form a ball). (Mixture may appear crumbly but will stick together when pressed between fingers.)
Place half of dough into a 1-cup measuring cup, pressing to compact dough. Remove dough from cup, and form into a ball. Divide ball into 6 equal portions. Repeat procedure with remaining dough. Cover and chill 15 minutes.
Place each dough portion between 2 sheets of plastic wrap. Roll each dough portion, still covered, into a 5-inch circle; chill until ready to use.