How to Make It
In a medium bowl, combine the flour with the salt. Using a pastry blender or 2 knives, cut in the butter until the mixture resembles coarse meal. Add the egg and water and mix with a fork until a dough forms. Turn the dough out onto a lightly floured work surface and pat it into a disk. Wrap the dough in plastic and refrigerate until firm, at least 1 hour or overnight.
On a lightly floured surface, roll out the dough to a 13-inch round. Fold the dough in half and carefully transfer it to an 11-inch tart pan with a removable bottom. Unfold the dough and gently press it into the pan without stretching. Trim the overhang. Wrap the tart shell in plastic and refrigerate it until firm, about 1 hour, or overnight.
Preheat the oven to 350°. Line the tart shell with foil and fill with pie weights, dried beans or rice. Bake the shell for about 1 hour, or until lightly browned around the edge. Remove the pie weights and foil and bake the shell for 10 minutes, or until evenly browned and cooked through. Transfer to a rack to cool. Leave the oven on.
In a medium saucepan of boiling salted water, cook the asparagus until tender, about 4 minutes. Drain and rinse under cold running water. Drain again and pat dry with paper towels. Arrange the asparagus in the tart shell with all the spears facing the same direction; trim them to fit if necessary.
In a medium bowl, whisk the eggs to mix. Beat in the milk, melted butter and salt. Pour the custard mixture over the asparagus and sprinkle the Parmigiano-Reggiano over the top. Set the tart on a baking sheet and bake for about 45 minutes, or until the custard is just set. Transfer the tart to a rack to cool for about 10 minutes, then cut into 8 wedges and serve warm or at room temperature.