To Make the Pâte Brisée: Place the flour, sugar, and salt in the bowl of an electric mixer fitted with the paddle attachment and combine on low speed. Add the shortening and butter to the dry ingredients. On low speed, cut the butter and shortening into the mixture until it looks coarse and crumbly. If you like, remove the bowl from the mixer and break up the fat particles with your fingers to distribute the fat more evenly. Add just enough ice water to combine and form the mixture into a ball.

Remove the dough from the bowl and place it on a clean, dry work surface. Then, with the heel of your hand, smear a small amount on the work surface by pushing it away from you until the dough appears homogenized—that is, smooth and not crumbly. Continue smearing small portions of it until all of the dough has been smoothed. This should take about 3 minutes. Shape the dough into a disk.

Position a rack in the middle of the oven and preheat the oven to 275°F.

To Make the Tartlet Shells: Roll out the dough on a lightly floured work surface to 1/8-inch thickness. Use a 4-inch round pastry cutter to cut out 12 rounds. Without stretching the dough, use a metal spatula to lift the rounds and fit them inside twelve 4-inch tartlet pans. Use your fingertips to press the dough firmly onto the bottoms and against the sides of the pans to thin the dough and so there will be excess going up the sides. Use the back of a knife to trim off any excess dough around the edges. Refrigerate for at least 1 hour, covered with plastic wrap, or until well chilled and firm. Or place in the freezer for 1 day and bake frozen.

Line the shells with aluminum foil and fill them with uncooked rice or dried beans. Place the tartlet shells on an 18 × 13-inch half-sheet or jelly-roll pan. Bake for 20 minutes, rotate the pan from front to back, and bake for another 20 minutes, or until the shells are lightly brown in color and firm to the touch when you lift the foil. Remove from the oven and immediately lift the foil with its contents from each shell.

Let the shells cool in their pans on a cooling rack for just 10 minutes, then remove from the pans and cool completely on the rack. If a shell seems to stick to its pan, turn the shell over into your hand and gently tap the bottom with your other hand to help release it. These shells are fragile, so pack carefully, stacking no more than two together if not using right away. These can be frozen or refrigerated in an airtight container for later use. Just pop them into a 275°F oven for about 1½ minutes, or microwave for 10 to 15 seconds.

To Make the Filling: Plump the raisins in the hot water for 5 minutes. Meanwhile, cream the butter and sugar at low speed in the bowl of an electric mixer fitted with the paddle attachment until light and fluffy. Drain the raisins and add to the butter mixture along with all the remaining ingredients, beating until well mixed.

Preheat the oven to 325°F.

To Make the Chess Cakes: Place the tartlet shells on an 18 × 13–inch half-sheet or jelly-roll pan and fill each two-thirds full with filling. Bake for about 20 minutes, or until set. Transfer the tartlets to a cooling rack, and serve warm or at room temperature.