Place the flour, butter, sugar, and salt in a food processor and pulse a couple of times until the butter is pea-sized.
Add the egg and pulse again until the dough starts to come together; if necessary, add a little ice water so that the dough coheres.
Bring the dough together with your hands and knead it a couple of times until it's smooth. Wrap it in plastic and chill it for half an hour.
Once it has chilled, divide the dough in two balls and roll out each part out as thinly as possible.
Cut each piece of dough into eight rectangles, about 3 x 4 inches in size. You may have to re-roll the scraps to get the eight, but it should work.
Place eight of the rectangles on a baking sheet and add a heaping teaspoon of jam or the filling of your choice to the center of each. Place one of the other rectangles over each filling-topped pastry and press down to seal the edges.
Use a fork to get a pretty pattern on the sides, then prick a few holes in each pastry so that the steam can escape.
Place the pastries in the freezer until they're firm. Meanwhile, preheat the oven to 350° F. When you're ready to bake, brush the pastries with a little beaten egg or milk and put them in the oven for 20 to 25 minutes, until golden brown.
Remove to a wire rack to cool. If you want to eat them like a real Pop Tart, enjoy them straight from the oven, while the filling is so hot that it burns your mouth.
Or, leave them to cool a little while you make the glaze by mixing together the powdered sugar and a little hot water or milk until you have a dollop-able consistency. Spread the pastries with the glaze and top with colorful sprinkles.