Preheat oven to 350 degrees F. Shred the squash on the large holes of a box grater, into a colander. Sprinkle with a heaping tablespoon salt and toss well. Place in the sink and drain for 15 minutes. Rinse and the squeeze firmly, by the handful, to remove excess water. Set aside.
Meanwhile, pulse bread into crumbs in a food processor. Heat 2 tablespoons olive oil in a large skillet over medium heat; add bread crumbs and stir until evenly toasted, about 5 minutes. Evenly spread crumbs in a 9-inch glass or ceramic pie pan. Place pan on a baking sheet.
Wipe out the skillet, add remaining 2 tablespoons oil, the onions and garlic and season with 1/2 teaspoon salt, cook over medium-high heat, until onions are start to brown, about 5 minutes. Add the zucchini, and cook, stirring, for 2 minutes. Stir in parsley, dill and marjoram or oregano. Remove from heat, cool slightly.
Whisk half-and-half, eggs and yolks in large glass measuring cup. Season with salt and pepper to taste. Spread the zucchini mixture in the prepared pan. Crumble the goat cheese and evenly scatter on the vegetables. Sprinkle Gruyere on top and pour the custard over the fillings.
Bake until the quiche is just set in the center, about 40 to 50 minutes. Cool completely on a rack before serving.
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