Preheat the oven to 350°F. Unroll one pie crust on a clean work surface. Brush the top lightly with water. Unroll the remaining pie crust and place on top. Roll the crusts into a 12-inch circle.
Fit the crust into a 10-inch deep-dish pie pan. Fold the edges under and crimp. Ball up a piece of parchment paper, straighten out, and place inside the crust. Fill with pie weights and bake for 15 to 18 minutes or until the crust is cooked. Remove from oven and let cool. Reduce the oven temperature to 325°F.
Meanwhile, whisk together 5 the eggs, half and half, mayonnaise, salt, pepper, and nutmeg in a medium bowl (with a spout for easy pouring if you have it). Separate the remaining egg and add the egg white to the filling mixture. Reserve the egg yolk for the egg wash.
Arrange the asparagus pieces, ham, shallot, and cheese in the bottom of the crust.
Pour the custard over the filling ingredients. Whisk the egg yolk and 1 teaspoon water in a small bowl. Brush the egg wash over edges of the crust. Bake the quiche at 325°F for 35 minutes or until set. Remove from the oven and let the quiche cool slightly before cutting into wedges and serving.