Place an oven rack in the center of the oven and preheat to 450 degrees F.
Unroll the crust on a lightly floured work surface. Using floured fingertips, seal any tears in the dough. Sprinkle the dough very lightly with flour. Using the bottom paper to lift, turn the dough over into 9-inch-diameter ceramic or glass pie dish. Peel off the remaining sheet of paper. Trim the dough overhang to 3/4 inch. Fold the overhang under and form a smooth top edge. Crimp the edge decoratively. Pierce the bottom and sides of the crust all over with a fork. Chill the crust at least 10 minutes.
Bake the crust until deep golden around the top edge and light golden on the bottom, about 10 minutes. Set aside to cool.
Reduce the oven temperature to 375 degrees F.
Heat the olive oil in a large nonstick skillet over medium-high heat. Add the pancetta cook until brown and crisp. Using a slotted spoon, transfer to paper towels to drain and cool, reserving the pancetta drippings in the skillet.
Add the zucchini, shallots and garlic to the skillet. Saute over medium heat until the zucchini is just barely tender, tossing occasionally, 5 to 6 minutes. Cool the zucchini slightly, about 10 minutes.
In a medium bowl, whisk the eggs and cream. Add the cheese, basil, cooled pancetta, mustard, salt, pepper, nutmeg and cooled zucchini mixture. Whisk to blend. Pour the custard into the cooled pie crust.
Bake the quiche until the sides are slightly puffed and brown and the center is set, 35 to 40 minutes. Cool on a rack 20 to 30 minutes, and then serve warm or let cool completely and serve at room temperature.