In the bowl of a food processor, add flours, sugar and salt; pulse until combined. Add butter and pulse until coarse crumbs form. Slowly trickle water into spout while pulsing food processor, adding just enough water til a dough just begins to form. Remove dough from processor and knead a few times on counter top. Divide dough into two discs. Roll each disc between 2 pieces of wax paper into a 1/4-inch disc; place discs, still covered by wax paper, on a baking sheet. Freeze dough until firm, about 1 hour.

Heat oven to 350 degrees F. Line two baking sheets with parchment paper or silicone mats. Using a 1 1/2-inch round cookie cutter (or whatever size you have, though obviously the larger the cookie cutter, the fewer cookies), cut dough into small round discs. Place discs about 1 inch apart on prepared baking sheets. Brush tops with egg wash, then sprinkle liberally with sesame seeds.

Bake cookies until lightly browned, about 15-20 minutes, rotating halfway through. Let cool on baking sheet 3 minutes, then transfer to a cooling rack to cool completely.