Step 1

In a food processor, pulse both flours with the salt. Add the butter and pulse until the mixture resembles coarse meal. Drizzle the ice water on top and pulse until the dough just comes together. Turn the dough out onto a work surface, gather up any crumbs and pat the dough into a disk. Wrap in plastic and refrigerate until well chilled, about 1 hour.

Step 2

On a lightly floured work surface, roll out the dough to a 14-inch round, 1/4 inch thick. Ease the dough into a 9-inch round, 2-inch-deep cake pan; do not trim the overhanging dough. Refrigerate until firm, about 30 minutes.

Step 3

Preheat the oven to 350°. Line the pastry with parchment paper and fill with pie weights. Bake for 20 minutes, until barely set. Remove the parchment and pie weights. Bake for 15 to 20 minutes, until lightly browned. Let cool on a rack. Increase the oven temperature to 425°.

Step 4

On a rimmed baking sheet, toss the brussels sprouts with the olive oil. Roast in the oven for about 20 minutes, tossing once, until browned and tender. Let cool, then coarsely chop. Reduce the oven temperature to 325°.

Step 5

In a bowl, whisk the milk with the cream, egg yolks, eggs, salt, white pepper and nutmeg. Stir in the brussels sprouts and scallions. Sprinkle the Gruyère in the crust and pour the filling on top. Set the cake pan on a foil-lined baking sheet and bake the quiche for about 11/2 hours, until set. Transfer to a rack and let cool for 30 minutes. Using a paring knife, trim the excess crust and discard. Cut the quiche into wedges and serve.