Make crust: Whirl 1 1/2 cups flour and the salt in a food processor to blend. Add butter; pulse until mixture looks like cornmeal. Add 1/4 cup ice water; pulse again until dough comes together, 30 seconds. Press dough into a disk, wrap in plastic wrap, and chill at least 1 hour and up to 1 day.
Unwrap dough and let warm up 15 minutes. With a floured rolling pin, roll into a 12-in. round. Press round onto bottom and up sides of a 10-in. deep-dish pie pan. Fold under the crust overhang on pan rim; crimp edge. Chill 30 minutes. Put oven rack on lowest rung. Preheat oven to 325°.
Line crust with parchment paper and fill with pie weights or dried beans. Bake crust 25 minutes; remove weights and parchment and bake until crust is slightly browned, about 10 minutes more. Remove crust from oven and set on a rimmed baking sheet. Raise oven temperature to 375°.
Make filling: In a large frying pan, heat oil over medium heat. Add garlic, fava leaves, green onions, parsley, and salt and cook, stirring often, until leaves are wilted, about 4 minutes. Chop mixture coarsely, then arrange over bottom of warm crust.
Make custard: Heat milk and cream in a large heavy-bottomed saucepan over high heat until mixture begins to simmer. Remove from heat. Put eggs in a blender with half of hot milk mixture and whirl for a few seconds. Whirl in salt and remaining milk mixture. Pour custard into crust, being careful to keep greens evenly distributed.
Bake quiche until slightly browned around edges and beginning to puff in center, 25 minutes. Let cool until warm or room temperature before serving.