In a bowl of a food processor, add the flour, salt, baking powder and the butter and process for 5-8 seconds. Until the butter is about the size of small peas.
Add the cream cheese and pule for 8 times, 2 seconds each pulse.
Remove the lid and sprinkle over the mixture the apple cider vinegar and ice water.
Pulse for again for about 8-10 times, each 2 seconds. Test the dough by pressing a small amount in the palm of your hand. If it comes together, it is ready. If it is still very dry and crumbles, pulse in another 1-1 1/2 ice water.
Place the mixture over a large piece of plastic wrap, then press it into a ball while holding the ends of the wrap.
Divide the dough into two, wrap each part with plastic wrap, shape it into discs, and refrigerate for a minimum of 60 minutes or up to three days.