Put the water and sugar in a small saucepan over medium-high heat and cook until the sugar completely dissolves and the liquid is clear, making a simple syrup. Pour into a glass pitcher or bowl to cool to room temperature. You can expedite the cooling process by putting in the fridge. 

Once the simple syrup has cooled, pour it into the bowl of a food processor fitted with a metal blade. Add the frozen raspberries (straight from the freezer) and run the processor for 1 minute, scraping down the sides as needed). Add the egg whites and let it run another 1 to 2 minutes until the mixture turns a pale pink color with a luscious texture, scraping the sides and bottoms as needed.

Serve immediately (it will be very soft and quite delicious) or spoon it into a freezer-friendly container (I use a loaf pan), cover with plastic wrap, and freeze until firm, at least 3 hours.