Refrigerate pineapple chunks until very cold, at least 1 hour or overnight.
Blend pineapple, 1 cup ice, yogurt, 1 tablespoon finely chopped ginger, honey, and lemon juice in a blender. Add up to 1/4 cup water, 1 tablespoon at a time, until mixture is smooth and thinned to desired consistency. Blend in mint leaves. Garnish with mint sprigs. (original recipe for papaya, but we couldn't find any in the store. If you have some, try it!)