The 'official' versions are made from packaged granita/slush mix with the booze added in, in granita/margarita machines...
However.
When trying to approximate them at home, we've landed on this as a suitable facsimile:
~2 cans (12oz or so each, standard frozen kind) of concentrate - for the grey goose one, use one each of lemonade and limeade; for the grand marnier one use 2 of oj
~2 cups of simple syrup (to make your own, boil 2 cups of water and dissolve 2 cups of sugar in it, then cool before mixing it in)
~2 cups of liquor - grey goose citron (absolut citron or stoli lemon work as well) for the lemonade slush; grand marnier for the other, obviously
~6 cups of cold water or half water-half ice mixture
For a quick prep, do not thaw the concentrates, use water-ice mix for the last part, and blend everything together (half at a time - it won't all fit in a blender at once). Serve.
For the more developed flavor, thaw the concentrates, use water only for the last part, and mix everything together. Then place in the freezer for several hours (we do it overnight), stirring a couple of times as it freezes. To serve, scoop the frozen slush into glasses and pour a little Sprite or club soda over it to give it a little extra sparkle.
