Papaya has a slight muskiness that makes it a good partner for both mild and assertive ingredients. Coupling it with mint gives this quick-to-fix smoothie a bright, clean taste.
Refrigerate papaya until very cold, at least 1 hour or overnight.
Blend papaya, ice, yogurt, 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.