Preheat the oven to 190°C.
For the chive pie crust: Mix the flour, chives and salt in a bowl. Add the butter and vegetable shortening and work them into the flour using a pastry cutter until the mixture resembles tiny pebbles. Using a fork, stir in the vinegar, beaten egg and 5 tablespoons cold water. Stir the mixture until just combined. Shape the dough into 2 discs. (You'll only be using 1 disc for this recipe. You can wrap the additional dough in plastic wrap for storage; it will keep up to a week in the fridge or up to 6 months in the freezer.)
Have ready 2 sheets of parchment paper that are each at least 12 inches square. Place the disc of dough between them. (If the dough is sticky for any reason, don't worry. Just sprinkle some flour on the parchment to get started. You shouldn't have to add much for it to stop sticking.) Starting at the center, roll the pin out to the edge. Turn the dough and parchment as necessary and continue rolling, always from the center to the outer edge. After a couple of rolls, lift the parchment paper away from the dough to loosen and replace the parchment. Flip the whole thing and loosen the other paper sheet. Continue rolling until the dough is large enough for your pie pan.
For the filling: Slice the leeks thinly, and then soak them in cold water for about 10 minutes to remove any grit or dirt. Drain well.
Put the mushrooms on a large baking sheet. Roast until golden brown, 15 to 20 minutes. Set aside.
Meanwhile, in a large skillet over medium heat, saute the leeks in the butter until golden brown and beginning to caramelize, 8 to 10 minutes. Set aside.
For the quiche base, add the cream and eggs to a medium bowl and whisk them to combine. Stir in the leeks, mushrooms, grated Swiss and some salt and pepper. Mix in the pesto and prosciutto. The mixture should be very thick!
Pour the mixture into the pie shell, then cover loosely with a sheet of aluminum foil to prevent it from getting too brown on top. Bake for 45 minutes, then remove the foil and bake for an additional 10 minutes. Remove from the oven and allow the quiche to sit for at least 10 minutes before serving.
Place the quiche on a cutting board and slice wedges with a serrated knife. Delicious for breakfast, and even better for lunch with a salad and a bunch of juicy grapes!