In a blender, blend raspberries and lime juice. Using a fine mesh strainer, strain out the seeds.
Meanwhile, in a small pot, stir sugar and water over medium heat until sugar dissolves. Increase heat and boil 3 minutes. Remove from heat and allow to cool slightly, about 20 minutes.
Stir the warm simple syrup into the raspberry and lime mixture. Cool in the fridge for 2-4 hours.
Freeze in an ice cream machine according to machine directions. (I freeze for roughly 15-20 minutes).
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