Preparation

Make the crust:

• Put the flour and salt in a food processor; pulse to combine. Add the butter cubes and pulse until they’re the size of extra-large peas (about 10 quick pulses). Add the shortening and continue pulsing until the largest pieces of butter and shortening are the size of peas (10 to 15 more quick pulses). Sprinkle 2-1/2 Tbs. of the water over the flour mixture and pulse a few times until the mixture just begins to come together. It should look rather crumbly, but if you press some between your fingers, it should hold together. (If it doesn’t, sprinkle on another 1/2 Tbs. water and pulse a few more times.) Dump the crumbly mix onto a lightly floured surface and press the dough into a 1-inch-thick disk. Wrap in plastic and chill for 30 minutes.
• On a lightly floured work surface, roll the dough into a round that’s 1/8 inch thick and 12 to 13 inches in diameter. Drape the dough around the rolling pin and ease it into a 9-inch pie pan. With kitchen shears, trim the overhang to 1/2 inch. Fold the overhang under and crimp it to build up an edge. Prick the crust with a fork in several places. Cover with plastic and refrigerate for 30 minutes. Meanwhile, position an oven rack on the middle rung and heat the oven to 350°F.
• Grease one side of a sheet of foil with cooking spray, oil, or butter. Line the pie pan with the foil, greased side down, and fill it with pie weights or beans. Bake until the edges of the crust look dry and start to turn golden, 25 to 30 minutes. Carefully remove the foil and weights; continue baking until the entire crust is deeply golden brown, another 15 to 20 minutes. Let cool on a rack.

Make the filling:

• In a medium bowl, whisk the condensed milk, egg yolks, lime juice, and grated zest. Pour into the cooled pie crust and bake at 350°F until just set, about 30 minutes. The center may still be a bit jiggly. (Use an instant-read thermometer to double-check the doneness; the center of the pie should be at least 140°F.) Let the pie cool thoroughly on a rack and then cover with plastic and refrigerate to chill completely, at least 3 hours but no longer than a day.
• Just before serving, whip the cream and sugar until stiff peaks form. Spread the cream on top of the pie, garnish with the strips of lime zest strips, and serve.