Combine flour, sugar and salt in a food processor; pulse a few times. Sprinkle butter over top and pulse until butter pieces are about the size of coarse crumbs. Scatter ice water over and pulse again a few times until a shaggy dough forms.
Turn dough out onto a floured counter. Gather the dough into a cohesive lump and pat it into a disc. Wrap dough in plastic wrap and refrigerate overnight, or for at least two hours.
To make filling:
In a medium bowl, stir together the chopped rhubarb, sugar, and flour. Let it sit for 10 minutes to start drawing out some of the juices while you roll out the dough.
To assemble and bake:
Preheat oven to 400º F. Line two baking sheets with parchment paper.
Roll dough into a rectangle (approximately 16 by 11" wide). Trim edges to make straight lines. Use a knife or pastry wheel to cut dough crosswise into 6 equal strips.
Divide the rhubarb filling among the dough strips, placing it in a small pile on one end of each rectangle, then fold remaining dough over and pinch edges to seal. Use a sharp paring knife to cut two 1" slits in the tops of each pie. Transfer pies to parchment-lined baking sheet.
In a small bowl, whisk egg with 2 tsp water. Brush pies with the egg wash. Bake pies for about 25 minutes, until golden brown and filling is bubbling out.
To make icing:
Whisk together confectioners’ sugar, vanilla extract and water. Drizzle over warm pies in a zigzag fashion.