This was what I originally started with earlier this week when I set out to create an Italian Ice. But I felt the lime overpowered the raspberry (specifically the AMOUNT of lime) so I left it in the freezer while I continued to think about it. The raspberries weren't cheap, you know, and I hated to throw the whole thing out. And I kept remembering my culinary instructor telling me "when you make a mistake, find a way to make it work for you". Then I remembered hardlikearmour's delicious Lime in the Coconut Float and so in went a can of coconut milk. Then I was afraid the raspberry flavor was getting upstaged, so, inspired by lapadia's Raspberry Coconut Cream Pie, in went a cup of fresh raspberries and voila, a fabulous sherbet that I can't stop eating now. Sometimes it takes a village. It's really unusual and unusually good! One tip: make it the day before you plan to devour it for best results!
Note on the egg white: I haven't made this without the egg white, but you could likely eliminate. The result will be the texture will be a little harder and not quite as smooth or creamy. —TheWimpyVegetarian
Combine 4 cups of the raspberries with the next 3 ingredients in a heavy pot and smash the raspberries with the bottom of a ramekin or potato masher.
Add the rest of the ingredients EXCEPT the egg whites and coconut milk. Bring to a boil and reduce to a simmer. Simmer until the berries completely break down into the liquid, about 10 minutes. Bring to room temperature and strain through a chinois to remove all the seeds, zest and mint leaves.
Whip the egg whites until they have soft peaks. Add them to the strained raspberry puree. Use a whisk to thoroughly mix.
Pour into an 8" X 11" pyrex baking pan or something similar. The depth of the puree should be somewhere between 1" and 2" deep. Pop into the freezer for a couple hours. After a couple hours, there should be partial freezing, especially around the edges. Taking a spoon, mix the partially frozen part with the non frozen. Keep checking it every 30 minutes or so, stirring it each time to completely mix the frozen part in.
When the raspberry ice is pretty solid, remove from the freezer. Empty a can of coconut milk into the bowl of a standing mixer fitted with a paddle attachment and mix it for a minute on medium speed in case the milk has separated. Then add the raspberry ice mixture and mix on medium-high to completely mix for about 1 minute. Fold in the last cup of fresh berries. Pour it back into the baking pan and return to the freezer for 2 hours or until frozen.
Before serving, place individual serving bowls in the freezer for at least 30 minutes. Scoop out some sherbet and enjoy!