Place 4 layers of cheesecloth in a fine-mesh strainer set over a large bowl. Add the yogurt and cover with the cheesecloth overhand. Place a plate or pot lid on top of the cheesecloth and secure with a weightA 16-ounce can from the pantry should do.. Refrigerate for at least 4 hours or up to overnight. The desired consistency is that of soft cream cheese.
Combine the drained yogurt, sugar, corn syrup, lemon juice, lemon zest, and fresh ginger in a large bowl. Transfer mixture to ice cream maker and process per manufacturer's instructions until the mixture reached the consistency of soft-serve ice cream, about 25 minutes.
During the last minute of mixing, add the crystallized ginger. Transfer the frozen yogurt to an airtight container and freeze for 2 hours before serving.