Store the cooled Yogurt Cake in an airtight container at room temperature for up to 2 days. Place a sheet of parchment between the cake and the lid if the top feels slightly tacky. For longer storage, refrigerate the cake in an airtight container for up to 5 days. Refrigeration can firm the crumb, so allow individual slices to stand at room temperature for 20 to 30 minutes before serving.

To freeze, leave off the powdered sugar and wrap the completely cooled cake, or individual slices, tightly in plastic wrap. Place the wrapped cake in a freezer-safe container or bag and freeze for up to 2 months. Thaw it overnight in the refrigerator, then bring it to room temperature before serving. Add the powdered sugar only after thawing.

The cake can be baked one day ahead: Once completely cool, cover it tightly and store it at room temperature. Dust it with powdered sugar shortly before serving so the surface remains neat and dry.