Preheat oven to 425 degrees and place baking sheet in oven to warm.
Cook white part of the onions in oil until soft, about 4 minutes. Allow to cool.
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).
Mix the green part of the onions with the white. Add half the grated cheese and spread over bottom of pan.
Beat the eggs into the milk and pour over onions and cheese.
Sprinkle with remaining cheese and paprika.
Place the quiche on the warmed baking sheet and cook for ten minutes.
Lower temperature to 375 degrees and bake 25-30 minutes, until just set.