Preheat oven to 425 degrees. On a lightly floured work surface, roll out the pastry dough into a round 12 inches in diameter. Drape the round over the rolling pin and carefully transfer to a 9-inch pie pan. Gently ease the pastry into the pan. Trim the pastry even with the pan rim. Prick the bottom and side of the pastry shell with fork tines. Form a double-thick 12-inch square of aluminum foil, poke a few holes in it, then press it into the pastry-lined pan. Bake for 8 minutes. Remove foil and bake until the pastry looks dry but not brown, about 4 minutes longer. Remove from the oven.

Reduce the temperature to 325 degrees. Bring a saucepan 3/4 full of lightly salted water to a boil. Add the broccoli and cook until tender-crisp, about 5 minutes. Drain well, pat dry, and set aside. In a bowl, using a fork, beat the eggs until lightly frothy. Stir in the green onions, milk, salt, pepper, and nutmeg. Scatter the broccoli evenly in the pastry shell. Drop small clumps of the cheese evenly among the florets. Carefully pour in the egg mixture.

Bake until a knife inserted into the center comes out clean, about 60 minutes. If the edges are browning too quickly, cover them with strips of aluminum foil. Transfer to a rack to cool for 15 minutes. Serve warm.