Whisk together the flour, baking powder, and salt in a medium bowl. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the sugar and vegetable shortening on medium speed until light. Reduce speed to low and add the eggs 1 at a time. Stop and scrape down the sides of the bowl. Add the flour in three installments, alternating with three installments of the milk. Add the vanilla during the last milk installment.
Form the dough into a log and place widthwise onto a 13-by-17-inch piece of parchment or waxed paper, and fold the paper over the dough. Using a half-sheet pan as a wedge, roll the dough into a log. This procedure tightens the log into a clean cylinder. Remove the waxed paper and slice dough into 16 (2-inch) rounds. Place on the half-sheet pan, cover, and chill for 1 hour.
Set two racks in the middle third of the oven and heat to 350ºF.
After the dough has chilled, roll each round outThink of this as more of a cookie dough — don’t worry about working it too much. to a 5- to 6-inch circle between two sheets of parchment or waxed paper. Fold over the edges of each round to create a rectangle. Roll out each rectangle to abut 1/4-inch thickness.
Match the 16 rectangles into 8 matching pairs. Brush one rectangle with the egg wash and top with 1 tablespoon of the jam, fruit butter, or preserves, spreading into an even layer about 1/2 inch from the edge. Top with another pastry rectangle. Use a fork to seal the tart by crimping the edge. Gently prick the top of the tart with the fork. Repeat with remaining dough and filling.
Bake for 25 minutes on a parchment paper-lined half-sheet pan until the edges just begin to brown. Remove to a wire rack to cool for 15 minutes. Enjoy warm, or cool thoroughly before storing in a zip-top bag for up to 1 week. Leftovers can be reheated in your friendly neighborhood toaster.
If you want to frost your tarts, slowly whisk the confectioners’ sugar and whole milk together in a small bowl. Paint the mixture onto the cooled tarts. Allow to dry before stacking, storing, and snarfing.