Pie dough:
1½ cups all-purpose flour
1½ tsp. cornstarch
½ tsp. salt
10 Tbsp. (1¼ sticks) cold unsalted butter, cut into ½-inch cubes
2 tsp. white vinegar
1/3 cup cold water
Filling:
2/3 cup packed light brown sugar
1/3 cup maple syrup
4 Tbsp. unsalted butter, very soft
1 large egg
1½ tsp. white vinegar or apple cider vinegar
1 tsp. vanilla extract
¼ tsp. salt
Small handful of raisins, dried currants, chopped pecans, or chopped walnuts (optional)
Pie dough:
Combine the flour, cornstarch, and salt in a large bowl. Scatter the fat on a large flour-dusted plate. Measure the vinegar into a 1-cup glass measuring cup. Add cold water. Refrigerate everything for 10 to 15 minutes.
Transfer the dry ingredients to a food processor. Add all of the fat, then pulse the machine six or seven times, until the pieces of fat are roughly the size of small peas.
Pour the vinegar-water mixture through the feed tube in a 7- or 8-second stream, pulsing the machine as you add it. Stop pulsing when the mixture is just starting to form larger clumps.
Turn the dough out onto your work surface and pack it into a ball. Put the dough on a sheet of plastic wrap and flatten it into a 3/4-inch-thick disk. Wrap the disk and refrigerate for at least 1 hour before rolling.
Roll the dough as you would for most pies, about 1/8 inch thick or a tad thinner. Don’t worry about keeping it nice and round like you normally would.
Using a 4-inch-diameter cookie or biscuit cutter, cut the dough into as many circles as possible. Line each cup of a standard 12-cup muffin pan with one of the circles, gently nudging it down into the bottom creases of the pan. Try not to stretch the dough as you work; it can help to use something blunt, like a narrow jar, to nudge the dough. The top edge of the dough circle should come to about the middle of the cup. Gather the scraps and reroll the dough if you need additional circles. Chill the pan in the freezer for 20 to 30 minutes.
Adjust one oven rack so it is in the lower position, and preheat the oven to 425°F (220°C). Combine the sugar, maple syrup, and butter in a mixing bowl. Whisk briefly. Add the egg, vinegar, vanilla, and salt, and whisk again.
Set the muffin pan on your work surface. If you’re using the fruit or nuts, put a few pieces in as many of the shells as you wish, but don’t crowd them. Use a ladle or ¼-cup measuring cup with a handle to divide the filling evenly between the shells.
Bake for 15 to 18 minutes, until the filling bubbles and darkens somewhat.
Transfer the pan to a rack and cool for 5 minutes, then carefully run a butter knife around the edge to loosen each tart. Let the tarts cool in the pan, then remove. Store, refrigerated, in a single layer in a covered tin or container, but let them come to room temperature before serving.