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To make the crust: Whisk together the dry ingredients. Work the butter into the dry ingredients, sprinkle in the water, and mix gently just until the dough comes together. Shape the dough into a disk, wrap it, and refrigerate it for at least 30 minutes.
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Remove the dough from the refrigerator and roll it into a 14" circle. Place it in a lightly greased a 9” deep-dish tart pan or a 9” removable bottom or springform pan, folding any excess dough inward to reinforce the edges.
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Prick the bottom of the dough, then place it in the freezer for 20 to 30 minutes while you preheat the oven to 425°F.
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To make the filling: Sauté the vegetables (mushrooms, peppers, and onion) and salt in olive oil over medium-high heat until soft and lightly browned and most of the liquid has evaporated, about 10 to 15 minutes. Set aside to cool.
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To assemble and bake the quiche: Line the chilled crust with foil or parchment paper and fill it with pie weights or dried beans. Place the crust on a baking sheet (to catch any butter drips from the bottom of the pan). Bake the crust for 16 to 20 minutes, or until it's lightly browned around the edges.
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Remove the crust from the oven and gently remove foil or parchment with the weights or beans. Set aside.
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Combine the eggs, milk, and Pizza Seasoning. Set aside.
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Sprinkle about 1/3 of the shredded cheeses over the crust. Add the vegetables, then slowly pour in the egg-milk mixture. Top with the remaining cheese.
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Bake the quiche on the baking sheet for 30 to 35 minutes, adding a pie crust shield or foil after about 20 minutes if necessary to prevent the edges from over-browning. The filling should be set and the edges golden. A digital thermometer inserted into the center of the quiche should read 165°F.
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Remove the quiche from the oven and let it rest for 15 to 20 minutes before slicing.
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Store any leftover quiche, covered, in the refrigerator for up to three days.