Had a look at the recipe and it had no guidelines.
https://food52.com/recipes/32418-esmae-s-orange-almond-cake
Think of it as a sponge cake (which it is) and store accordingly.
Julia Child (in Mastering) has a similar orange-almond cake and some recipes for it suggest 4 days in fridge in air-tight container.
Hope this helps.
Stilltasty.com suggests 1-2 days room temp, week in fridge or 4-6 mo in freezer for most unfrosted cakes.
http://www.stilltasty.com/fooditems/index/18682
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https://food52.com/recipes/32418-esmae-s-orange-almond-cake
Think of it as a sponge cake (which it is) and store accordingly.
Julia Child (in Mastering) has a similar orange-almond cake and some recipes for it suggest 4 days in fridge in air-tight container.
Hope this helps.
Stilltasty.com suggests 1-2 days room temp, week in fridge or 4-6 mo in freezer for most unfrosted cakes.
http://www.stilltasty.com/fooditems/index/18682