Preheat oven to 350 degrees F (175 degrees C).
In a mixing bowl, combine crackers and 4 tablespoons of butter in a bowl until well blended. Press into the bottom and 1 inch up the sides of 8 inch pie plate to form a shell. Refrigerate until needed.
Melt remaining 2 tablespoons butter in heavy skillet over medium heat. Sauté onions and garlic slowly until tender, about 12 minutes. Arrange onions in the cracker crust.
Beat eggs, whole milk, chives, and salt in a bowl until blended. Pour the mixture over the onions. Sprinkle with cheese and paprika.
Bake in a preheated 350 degrees F (175 degrees C) oven for 35 minutes, or until a knife comes out clean. Garnish with the parsley. Serve hot or at room temperature.