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1
Preheat oven to 375u00b0F with rack in middle.
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2
Roll out dough on a lightly floured surface with a lightly floured rolling pin into a 13-inch round. Fit dough into pie plate, letting excess hang over edge. Fold overhang inward and press against side of pie plate to reinforce edge. Prick bottom all over with a fork. Chill until firm, about 30 minutes.
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3
Line pie shell with foil and fill with pie weights. Bake until pastry is set and edge is pale golden, 20 to 25 minutes.
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4
Carefully remove foil and weights, then bake shell until deep golden all over, 15 to 20 minutes more. Put pie plate in a 4-sided sheet pan. Leave oven on.
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5
While shell bakes, cook broccoli in a 3-quart pot of boiling salted water 4 minutes. Drain broccoli and rinse under cold water to stop cooking, then pat dry.
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6
Mince and mash garlic to a paste with a generous pinch of salt.
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7
Whisk together garlic paste, eggs, half-and-half, nutmeg, cayenne, and 1/4 teaspoon salt in a large bowl until smooth.
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8
Pour filling into pie shell and add broccoli, then sprinkle with cheeses.
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9
Bake quiche until custard is just set, 45 to 50 minutes. (Center will tremble slightly; filling will continue to set as it cools.) Cool at least 20 minutes.
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10
Serve quiche warm or at room temperature.
