Place all the ingredients, except the water and egg, in the work bowl of a food processor fit with a metal dough blade, or a medium bowl if making by hand. If using a food processor, pulse a bit to break up the butter pieces a bit more. If making by hand, use a mezzaluna or pastry blender to chop up the butter into small pieces, or smoosh and pinch them with your fingers. Another option is to grate frozen butter, and smoosh and pinch it into the flour.
Sprinkle 3 tablespoons of the water over the dough and mix and pulse by food processor, or fluff with a fork or your hands. Repeat with the remaining water in two additions.
Add the egg and pulse a few times if using a machine, or fluff it around with a fork, to mix into dough evenly.
Place the dough on a large piece of plastic wrap and tightly pull the edges up around it, pressing with the heels of your hands to moldthe plastic-wrapped dough into a ball. The ball can be cut in half, and each part wrapped separately in plastic wrap. Flatten the discs to a height of about ¾ inch (2 cm) and width of 6 inches (15 cm). It is easier to form balls or discs of gluten-free dough when they are wrapped and covered, rather than placing your hands directly on the dough.
Chill dough for 10 to 20 minutes in the fridge or even 5 to 7 minutes in the freezer, and roll as soon as possible.
When rolling out any gluten-free dough, the dough should be at a pliable temperature, about 64°F (18°C), and rolled between two layers of plastic wrap.