Add the flours, sugar, and salt to the bowl of a food processor. Pulse once or twice to combine.

Add the butter. Pulse a few times, just until the butter mixes into the flour, forming a sandy mixture with some pea-sized pieces.

Add the egg, vinegar, and water. Pulse 60 to 90 seconds until it comes together into a ball of dough. It’ll start out looking like wet sand, and comes together into a ball during the last few seconds of pulsing.

Dump the dough onto a counter (no need to flour unless you’re using the dough immediately, but note that this dough also doesn’t require any chilling time). Divide the dough into 2 equal pieces. Shape into 1-inch thick, round disk. Wrap tightly in plastic film, and chill up to 3 days.