Add the flour, sugar, and salt to the bowl of a food processor. Pulse a couple of times to combine.
Add the butter and vegetable shorting to the flour mixture. Pulse 5-8 times, until the mixture forms little balls, like moist crumbs. It’s important to pulse the food processor, not run it continuously so you don’t overwork the dough.
Dump the mixture into a bowl and sprinkle with 3 tbsp ice water. Use your hands to bring gently bring the dough together, tossing the flour-butter mixture with the water to moisten, then squeezing it together in your hands. Add more water, 1 tbsp at a time, until the dough comes together. The dough should be just past crumbly and just coming together. You don’t want it to be wet enough to be sticky.
Put the dough in the center of a large piece of plastic wrap and wrap tightly. Refrigerate for at least 30 minutes and up to 2 days.
Preheat the oven to 400 degrees.
Remove the dough from the refrigerator, unwrap and cut into 6 even pieces. Roll out the dough, one piece at a time, into circles that are approximately 3/8-inch thick. Gently lift each circle of dough and lay it over one mini tart pan. Press the dough into the tart pan, pressing it into the corners and allowing about 1-inch of dough to hang over the edge. The excess dough will help keep the dough from shrinking down into the pan as the crust bakes and will be cut off later.
Place the tart pans onto a baking sheet and line each with a small piece of aluminum foil. Fill each lined pan with pie weights or dried beans to weight it down.
Bake the crusts for 15 minutes. Remove the crusts from the oven and lift out the foil and pie weights or dried beans. Prick the bottom of the crusts several times with a fork. Return the crusts to the oven and bake for an additional 10-15 minutes, until the crusts are a rich golden brown. Remove from the oven and allow to cool on a wire rack while you make the lemon tart filling.
MAKE THE LEMON SABAYON FILLING:
Fill a saucepan with enough water to come about half way up the sides of the pan. Set it over high heat and bring to a boil.
In a metal bowl large enough to fit snuggly over the saucepan of water without sinking into the water, add the eggs, egg yolks, and sugar. Whisk to combine.
Place the metal bowl over the boiling water and whisk continuously for 2-3 minutes until the eggs are foamy and have thickened. (Alternatively, you can also use a hand held electric mixer. Beat on medium, continuously moving the beaters around the bowl.)
Add 1/3 of the lemon juice and continue to whisk vigorously until the mixture thickens again, another 2-3 minutes. Repeat this process 2 more times with the remaining lemon juice. After the third addition of lemon juice, whisk until the mixture is thick enough to where the whisk leaves a trail in the bottom of the bowl.
Turn off the heat, but leave the bowl over the water. Whisk in the butter, one piece at a time, waiting until each piece of butter is completely incorporated before adding the next. (If you’ve been using an electric mixer, switch to a wire whisk to add the butter.) The sabayon might loose some of its thickness as you incorporate the butter, but don’t worry – it will thicken back up as it cools. Whisk in the vanilla.
Pour the warm sabayon into the tart shells, distributing it between them evenly.
Preheat the broiler. While the sabayon is still warm, place the tarts on a baking sheet and put them under the broiler. Either keep the oven door slightly ajar, or turn on the light in your oven so you can watch the tarts. Leave them under the broiler just long enough to brown the tops. This will happen very quickly, so keep watch and do not walk away from the oven.[/I]
Remove the tarts from the oven and allow to cool to room temperature. Refrigerate until ready to serve.
Right before serving decorate with powdered sugar, if desired.