On a sheet of parchment paper or a well-floured surface, roll the dough out to somewhere between 1/8- and 1/4-inch (3- and 6-mm) thickness.
Using a 3- to 4-inch (8- to 10-cm) round or square cookie cutter, cut out as many shapes as you can. (If you don’t have a cookie cutter, an empty tuna can that you’ve washed and rinsed well will do the trick quite nicely.)
Working with 1 portion of dough at a time, place a scant teaspoon or so of your desired filling on half the dough. (If your dough is larger or smaller than 3 inches, you’ll need to use more or less filling accordingly.) Dip your fingertip in water and lightly wet the edge of the dough with a tiny bit of water. Fold the uncovered dough over the filling and press firmly to make a seal. Repeat with the remaining dough and filling. Use a fork or knife to poke a little vent on top of each pie.
Cover and refrigerate the hand pies until you’re ready to bake them, at least 15 minutes and up to several hours. (You can instead freeze the hand pies for baking another time. Simply place the hand pies on a parchment-lined baking sheet, making certain they’re not touching, and freeze overnight. Transfer the hand pies to resealable plastic bags. Thaw in the fridge prior to baking.)
Preheat the oven to 400°F (205°C).Lightly brush the hand pies with the egg white mixed with the water and sprinkle with a bit of sugar. Bake the hand pies until golden, 10 to 17 minutes, depending on the size of your hand pies. Let them cool slightly. Revel in them while they're still warm.