Preheat oven to 425°F | 220°C.Prepare dough. If you are making homemade dough, let it chill in the refrigerator for at least an hour. Roll dough out in batches on a lightly floured surface. Dough should be no more than ⅛-inch thick. Use a 3-inch biscuit cutter, cookie cutter, or drinking glass rim to cut circles.
Using your fingers, the end of the rolling pin, or a piece of scrap dough, form the dough into the muffin tin. Form a little rim around the top of the muffin cup, as you would form a crimping edge on a regular-sized pie. Use a smaller cutter to trim and clean up the edges of each tart.
Put the tarts into the freezer for 10-15 minutes before proceeding.
Put the frozen mini tart shells into the preheated oven (425°F | 220°C) oven and immediately reduce heat to 375°F | 190°C.Bake for 10-12 minutes and remove from oven. Tart shells should be very lightly browned.
Combine sugar, flour, cornstarch, salt, and water in a heavy saucepan. Place over medium heat and bring to a boil. Simmer the mixture until it becomes thick and translucent, stirring constantly. Remove from heat.
In a small bowl, whisk together egg yolks and lemon juice. Pour the egg yolk mixture into the hot sugar mixture in a slow stream, whisking constantly.
Return pan to heat and bring to a boil, stirring constantly. Remove the mixture from heat and whisk in lemon zest and butter. The lemon filling should be very thick at this point. Allow it to cool while you whip the meringue.
Whisk together cornstarch and cold water in a small microwave-safe bowl.Cook in the microwave on high for 1 minute, or until it thickens. (The mixture will be very thick.) Set aside to cool completely.
In a large mixing bowl, whisk the egg whites with the cream of tartar on medium-low until soft peaks form, slowly increasing the speed to medium as you do.Increase the mixer speed to medium-high, and gradually add the vanilla and the cornstarch mixture.
Add the sugar to the egg whites one tablespoon at a time, in a raining motion. Increase the speed to high and continue beating the egg whites until the meringue forms stiff peaks. Do not overbeat. The meringue is ready to bake when it has the consistency of shaving cream and forms stiff peaks when you remove the whisk.
Put filling in a pastry bag or resealable bag. Pipe filling into the prepared mini shells. Put meringue into pastry bag or resealable bag. Pipe a dollop of meringue onto the top of each tartlet.
Preheat oven to 325°F | 165°C. Bake mini tarts for 10-15 minutes, until tips of the meringues begin to brown.
Cool on a rack and serve or refrigerate.
Tip for Whipping Egg Whites: Always start whipping egg whites on at a lower speed. If they are beaten too quickly at the beginning, the structure of the foam will not be as strong, and they won't beat up as high as they should.Advanced Prep: You can make the pastry shells and lemon curd up to a day in advance. The meringue should be made immediately before baking.Refrigerating Mini-Tarts: When the mini-pies have completely cooled, they should be refrigerated if they are not eaten within 2 hours.