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Preheat oven to 425 degrees and place baking sheet in oven to warm.
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Cook white part of the onions in oil until soft, about 4 minutes. Allow to cool.
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Mix the flour with the salt and cut into the butter until the mixture looks like meal. Add just enough ice water to make a stiff dough. Roll out and put it into the bottom of a 8 inch quiche pan( pie plate will work too).
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Mix the green part of the onions with the white. Add half the grated cheese and spread over bottom of pan.
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Beat the eggs into the milk and pour over onions and cheese.
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Sprinkle with remaining cheese and paprika.
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Place the quiche on the warmed baking sheet and cook for ten minutes.
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Lower temperature to 375 degrees and bake 25-30 minutes, until just set.
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Allow to stand 10 minutes, cut and serve.