Move oven rack to lower-middle position and preheat oven to 350 degrees F.
MAKE ZUCCHINI FILLING: In large skillet over medium-low heat, heat oil until shimmering. Add zucchini, shallot, garlic, and salt and cook, covered, until onions are tender and zucchinis have released their liquid, about 7 minutes. Uncover and cook until bottom of pan is dry, stirring often, about 4-5 minutes. Transfer zucchini filling to medium bowl, toss with basil and flour and set aside to cool for 5 minutes.
MAKE CUSTARD: In large bowl whisk together eggs, half and half, salt, pepper, and nutmeg. Fold in zucchini filling and fontina and Parmesan cheeses. Place unbaked pie crust on top of baking sheet, and pour mixture into unbaked pie crust.
BAKE QUICHE: Bake until quiche is set and crust is golden brown, about 34-38 minutes. Cool on wire rack 20 minutes before serving.