Pour tigernuts and almonds into the pitcher of a high-powered blender. Cover them with hot water, and allow them to soak overnight at room temperature, at least 8 and up to 12 hours.
Add the strawberries to the blender, and blend the fruit, tigernuts and nuts together with the soaking water at two minutes.
Strain the horchata through cheesecloth and into a pitcher. Stir in jaggery or honey to sweeten the horchata to your liking. Transfer to the refrigerator to chill, and serve over ice. Strawberry horchata will keep up to one week.