In a food processor, add 1⅔ cups of the flour and pulse briefly to distribute it evenly at the bottom of the bowl. Arrange the butter pieces over the flour and pulse several times until the mixture starts forming clumps, ensuring there is no dry flour left.
Spread the mixture evenly in the food processor, then sprinkle in the remaining 1 cup of flour. Pulse again just enough to create a crumbly texture.
Transfer the mixture into a large bowl. Drizzle the ice water and apple cider vinegar over the dough. Using a spatula, gently fold and press the mixture until it starts to come together into a cohesive mass. If needed, use your hands to knead any remaining dry bits into the dough.
Divide the dough into two equal portions and shape each into a 1-inch-thick disk. Wrap each disk tightly in plastic wrap and refrigerate for at least 2 hours, or up to 48 hours.
To roll out the dough, place one chilled disk onto a lightly floured surface. Dust the top with flour and, using a rolling pin, roll it out evenly into a thin, large circle, approximately ⅛ inch thick. When placing an inverted pie plate over the dough, the rolled-out circle should extend at least 1 inch beyond the plate’s edges. Rotate the dough a quarter turn after every few rolls to prevent sticking. Lightly dust the surface as needed and flip the dough a couple of times during the rolling process.
To transfer the rolled-out dough, carefully roll it onto the rolling pin, then unroll it over the pie plate. Gently press it into the bottom and sides, ensuring a snug fit. Trim any excess dough, leaving a ½-inch overhang around the pie plate’s edges. Cover loosely with plastic wrap and refrigerate while rolling out the second dough disk.
Repeat the rolling process with the remaining disk, rolling it out into another thin, even circle of the same thickness.
Proceed with assembling and baking according to the pie recipe you are preparing.
Yields one 9- or 9½-inch double-crust pie or two single-crust pies.