In the bowl of a food processor, combine butter, flour, and salt, then pulse until it resembles a mixture of sand and peas. Whisk together cold water and whole egg; slowly drizzle into the butter-flour mixture 2 tablespoons at a time, pulsing as you go. When a ball of dough forms, stop adding liquid. It should be smooth and not sticky.
Place in a bowl, cover with a damp cloth, and refrigerate at least 1 hour before rolling out. Preheat oven to 450 degrees. On a lightly floured surface, roll out dough to fit a 9-inch quiche or deep-dish pie pan; lift and set in pan. Press into place, trim excess, and form a decorative edge. Prick the bottom and sides with a fork and bake until it takes on a light-golden hue, about 9 to 12 minutes, depending on your oven. Remove from oven and brush the egg white mixture over hot shell to seal it. Set aside.
For the filling:
In a medium sauta© pan, sauta© asparagus, shallots, and cremini mushrooms in butter over medium heat until softened, about 5 minutes. Sprinkle with ¼ teaspoon salt and set aside. In a separate pan, scald cream by bringing it to the steaming point over high heat. Remove from heat immediately and cool 3 minutes. Meanwhile, whisk together eggs, the remaining ¼ teaspoon salt, and white pepper. Then, in a very slow trickle, whisk scalded cream into eggs.
Preheat oven to 375 degrees. Spread cheese, chives, and sauta©ed vegetables on bottom of piecrust, pour in the egg mixture, and bake 35 to 40 minutes. Test for doneness by moving the pie back and forth. If it jiggles slightly, like set gelatin, iti¿½s done. Garnish with chives.