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1
In the bowl of a food processor, pulse together the flour, salt, butter, and shortening until the mixture resembles course crumbs. While pulsing, pour the ice water in a stream into the processor until the dough comes together in a ball. You can also do all this by hand with a pastry cutter if you prefer.
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2
Remove the dough onto a floured board. It will be a bit sticky. With floured hands, form the dough into a disk about 6 inches in diameter. Wrap with cellophane and refrigerate for about 45 minutes.
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3
After the dough has chilled, remove it from the fridge and place it back on the floured board. Flatten the disk with about 5-6 smacks of a rolling pin. Roll out into a circle about 1/8th of an inch thick and 12 inches in diameter. You should lift the dough a bit as you roll, and sprinkle with more flour if needed to keep it from sticking. Carefully transfer to a tart pan, pressing the dough into the bottom and sides. Fold any overhanging dough back into the sides of the pan to make the edges a bit thicker/sturdier. Place the tart pan in the freezer for about 20 minutes.
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4
Blind-bake the crust: Preheat the oven to 375 degrees. Take a large sheet of parchment paper (larger than the pan), place it onto the crust and cover with pie beads or dried beans. Make sure there is enough parchment paper sticking out to cover the edges of the tart as much as possible. Bake for about 25 minutes. Remove from the oven, discard the parchment paper with the beans, and allow the pan to cool slightly.
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5
Trim the stem of each sprout, discarding any outer leaves that fall off or become loose. Rinse the sprouts and cut them in half. In a covered saute pan, melt the butter on medium heat. Add the shallots, 1/4 tsp salt, black pepper, and 1/8 tsp of garlic powder, and saute on medium-low heat for about 3 minutes. Add the brussels sprouts to the pan and toss gently to coat them. Re-arrange them so that they are cut side down in the pan. Cover the pan and allow them to cook and get golden for about 15 minutes. Add the white wine, raise the heat to medium, and allow to cook, uncovered, for about 3 minutes more. Remove from heat and set aside.
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6
In a large bowl, beat the eggs with a wire whisk. Add the heavy cream and milk and whisk to combine. Add the remaining 1/2 tsp salt, white pepper, 1/2 tsp garlic powder, thyme, flour, baking powder, and grated pecorino cheese and whisk again. The mixture will have small lumps - that is ok! Add the chopped chives, dill, swiss and cheddar cheeses, and blend thoroughly. Pour the batter into the prepared tart pan.
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7
Spoon the brussels sprouts with the shallots on top of the batter, ensuring that they are spread out across the entire pan. Some of the sprouts will sink, but those that are resting on the surface should be positioned cut-side up.
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8
Place the tart pan on top of a baking sheet to catch any spillage in the oven (there really shouldn't be, even with that much liquid, but it will save you a mess if it happens). Bake the tart for about 40 minutes. It should be puffy, golden, and set in the middle.
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9
Allow the quiche to cool on a wire rack for at least 10 minutes before cutting. It will shrink slightly. Enjoy!
