To make the homemade tart dough: Combine flour and salt in a food processor; pulse it one time to mix. Add the butter pieces and pulse 4 times. Add shortening one tablespoon at a time and pulse each time you add a tablespoon. The mixture should resemble coarse cornmeal, with butter bits no bigger than peas.
Sprinkle 6 tablespoons of ice water over flour mixture one tablespoon at a time. Pulse once after you add each tablespoon of water. If you pinch some of the crumbly dough and it holds together, it's ready. If the dough doesn't hold together, keep adding water, a tablespoon at a time, pulsing once after each addition, until the mixture just begins to clump together.
Form into a disc: Clean off your counter really well or use a pastry board or a nice cutting board. Flour your hands generously. Take the dough out of the food processor. Tilt the rolling pin and sprinkle it with flour as you rotate the rolling pin. Divide the dough into two balls and flatten each into a 4-inch wide disks.
Sprinkle a little bit of flour on each disk and then wrap both separately in plastic wrap and refrigerate at least 1 hour before rolling. When you are flattening the disks, you are not working the dough. You are just simply flattening the shape into a disk. If you are making the pie that day, make sure you refrigerate for at least an hour. It can stay for up to 2 day in the refrigerator.
Prep the tart crust: When it is time to roll the dough out to make my pie, I take it out of the refrigerator and I usually let my dough sit out for about 5 minutes before rolling. It's hot here in Florida. Doesn't take more than 5 minutes to get to the perfect rolling temperature.
Using a rolling pin, apply light pressure while rolling outwards from the center of the dough. Every once in a while you may need to gently lift under the dough.
Roll dough out on a floured surface till dough is about 1/8″ thick
When the has reached the right size, gently fold it over your rolling pin and transfer to the parchment paper lined baking pan.
Make the Savory Tart: Preheat oven to 425 F.
Cook the potatoes and onions: Heat oil in a skillet over medium-high heat. Add onion, potatoes, thyme, salt and pepper; cook approximately 20 minutes.
Assemble the tart: Sprinkle the feta and other cheese in the center, leaving a 1 1/2 inch border; to a leave a 1 1/2 inch border around the edge.
Spoon on the potato/onion filling on top of the feta and other cheese in center.
Finish off the tart crust: Fold the border around the filling and make cute pleats. Leave the center open. Drizzle a tablespoon of olive oil on the top and sprinkle with a little salt and pepper.
Brush on egg wash: Brush the pleated dough with the beaten egg.
Bake the tart: at 425 F for 25 minutes or until golden brown. Cool for about 10 minutes.
If you need a different dinner idea, this savory tart is wonderful served with a mixed salad and maybe even a very nicely chilled glass of white wine.