In a large bowl, put the flour, salt, and butter cubes. Using the tips of your fingers, mix the ingredients until it resembles coarse cornmeal. Add the ice water a little at a time until the dough just comes together. Remove the dough from the bowl and form into a disk. Cover the disk with plastic wrap and put in the refrigerator to chill for 1 hour.
Preheat oven to 375 degrees F.
Lightly flour the work surface, roll-out the dough and put in a pan with a removable bottom. Allow the dough to hang over the edges. Trim the edges slightly, still leaving an overhang of dough. Poke or dock the bottom of the pastry with a fork.
Put the crust on a baking tray and cover the bottom of the pastry dough with aluminum foil. Fill the crust with dried beans or pastry weights and bake for approximately 15 minutes. Remove the aluminum foil and beans, and then put the pastry back in the oven until the bottom is golden brown, approximately 10 minutes.
Remove the pastry crust from the oven. While the pastry is still hot, brush a thin layer of quiche egg mixture over the bottom to seal.
For the quiche filling:
Preheat the oven to 375 degrees F.
Put the shallots in a small saute pan skin-side up and coat with olive oil. Season the shallots with salt and roast for 30 minutes, until tender. Reduce the oven temperature to 325 degrees F. Peel the skins from the shallots and set the shallots aside. Put the milk in a pot over low heat until scalded, set aside.
In a bowl, whisk the eggs, thyme, salt, and pepper until incorporated. Slowly whisk the warm milk into the egg mixture.
Scatter the roasted shallots and goat cheese into the base of the pastry crust.
Pour the egg mixture into the prepared quiche pastry crust. Bake in the oven for approximately 20 to 30 minutes, until the custard has set. Remove the quiche from the oven and allow to cool. Slice the quiche into portions and put the arugula and prosciutto over the quiche.