Bring eggs to room temperature by placing them in a bowl and running lukewarm water over them for about 5 minutes.
Using a stand mixer fitted with the paddle attachment, combine the butter, sugar, and salt and mix on medium speed until smooth. Mix in 1 egg. Add the remaining egg and mix until smooth. Stop the mixer and scrape down the sides of the bowl with a rubber spatula. Add the flour all at once and mix on low speed just until incorporated.
On a lightly floured work surface, divide the dough into 4 equal balls and shape each ball into a disk 1/2 inch thick. Wrap well in plastic wrap and chill for at least 2 hours or overnight.
To line a tart pan, place a dough disk on a lightly floured surface and roll out 1/8 inch thick, rolling from the center toward the edge in all directions. Lift and rotate the dough a quarter turn after every few strokes, dusting underneath as necessary to discourage sticking, and work quickly to prevent the dough from becoming warm.
Cut out a circle 2 inches larger than the pan. If the dough is still cool, carefully transfer the circle to the pan, easing it into the bottom and sides and then pressing gently into place. Do not stretch the dough, or the sides will shrink during baking. If the dough has become too soft to work with, put it in the refrigerator for a few minutes to firm up before transferring it to the pan. If the dough develops any tears, just patch with a little extra dough, pressing firmly to adhere. Trim the dough level with the top of the pan with a sharp knife. Place the pastry shell in the refrigerator or freezer until it is firm, about 15 minutes.
Preheat the oven to 325°F. Dock (make small holes in) the bottom of the tart shell with a fork or the tip of a knife, making tiny holes 2 inches apart. Place in the oven and bake for 7 to 10 minutes for a partially baked large shell. The pastry should be lightly colored and look dry and opaque. Check the shell(s) during baking and rotate the pans if necessary for even color. If you want to brush the shell(s) with a glaze (see headnote), beat the egg with the salt in a small bowl. A minute or two before the desired color is reached, remove the shell(s) from the oven and lightly brush the bottom and sides with the glaze. Return the shell(s) to the oven and bake until the desired color is reached and the glaze is set.
For a fully baked shell, proceed as directed for a partially baked shell, but bake until golden brown, about 5 minutes longer.
Let cool completely on wire racks. The pastry shells will keep, well wrapped, in the refrigerator for up to 1 week or in the freezer for up to 2 weeks.
Any leftover dough can be used as a simple cookie dough. This dough keeps exceptionally well, so make some for use now and freeze the rest for future use (it will keep for up to 3 weeks), either in disks or in rolled-out rounds. If you roll out all the rounds to freeze for future use, place a sheet of parchment or waxed paper between them to prevent them from sticking to one another when you thaw them.
This recipe can be easily halved.