Whirl flour with 2 tsp granulated sugar and salt in a food processor. Add butter. Pulse until finely crumbled. With machine still running, add water, 1 tbsp at a time, through the spout and continue whirling until a ball forms, 30 seconds. Divide pastry in half. Form into 2 discs. Wrap each with plastic and chill in refrigerator for 30 minutes.

Combine rhubarb with 1 cup granulated sugar in a large saucepan and set over high. Boil, then reduce heat to medium. Cook, stirring often, until mixture is very thick and reduced to 2 1/2 cups,  20 to 35 minutes. (Time will depend on water content of rhubarb.) Stir in vanilla and cool slightly, 5 minutes.

Position rack in lower third of oven. Preheat to 375F.

Beat egg with water in a small bowl. On a lightly floured surface, roll out 1 pastry disc into a 13-in. circle. Lift onto  a 9-in. metal pie pan set on a baking sheet. Press dough over bottom and  up sides of pan, leaving 1-in. overhang. Scrape rhubarb mixture into pastry. Brush overhang with egg wash. Roll out second pastry disc into a 12-in. circle, about 1/8 in. thick. Cut into 12  3/4-in. strips. Follow instructions for lattice top (below).

Brush lattice and overhang with egg wash. Sprinkle with coarse sugar. Bake  in lower third of oven until golden brown, 50 to 60 minutes. Transfer pie to a rack to cool completely, 1 hour.

To make lattice top:

1.  Lay 6 pastry strips vertically across pie.

2. Fold back every other strip, then lay a new strip horizontally.

3. Straighten folded strips back across pie. Fold back alternate strips, then place a new strip horizontally above the first one.

4. Repeat until pie is completely covered. Fold overhanging pastry over lattice strips to seal, and crimp edges inside the pan.