In your food processor combine flour, sugar and salt. Add the butter and pulse until you get a texture of coarse crumbs. Mix in eggs and vanilla. Pulse a few times until you get a more solid ball of dough.
Transfer to a large bowl. The dough should be soft, but not overly sticky. If it is, keep adding flour until it's smooth. Knead the dough into a smooth ball, then flatten it into a disk. Wrap in plastic wrap and chill in the refrigerator for 1 hour.
Preheat the oven to 350°F (175°C). Grease a square 12-inch (30-cm) baking pan, line it with parchment paper.
Place plums in a large bowl and sprinkle them with sugar and cinnamon. Stir to coat the plums and set aside.
Slice off 2/3 of the dough and transfer it to the pan. Stretch it out and press it into the bottom of the pan with your fingers as evenly as you can.
Spread plums all over, with the sliced side up. Sprinkle with one more tablespoon of sugar.
Lastly, flour your working surface and roll out the last 1/3 of the dough. Slice it into strips and gently lay them over the pie to form a net.
Bake for 45-50 minutes until the dough is golden brown and plums soft. Remove from the oven.
Mix apricot jam with a tablespoon of very hot water. Brush the warm plum pie all over with the jam, then allow it to cool completely before slicing. Sprinkle with powdered sugar before serving, if desired.