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Preheat oven to 325°F.
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To start, peel and chop persimmons into cubes and purée in a food processor, with orange juice. The more ripe the persimmon, the better. (gooey and honey-like is great for this step!). Set aside.
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In a mixer bowl, using the whisk attachment, mix eggs and sugar together. Once those two are well combined, add the cup of olive oil and sea salt. Continue mixing. Then fold in persimmon purée and sour cream.
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Prepare dry mix in a separate bowl by adding together flour, baking powder, baking soda, cinnamon, cardamom and nutmeg. Fold all into the mixer containing eggs and olive oil, bringing all the ingredients together.
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Thinly coat the inside of a 9 inch round pan or spring form with butter. Pour in the batter, and place in preheated oven for 45 minutes to 1 hour. (I suggest a toothpick test after 45 minutes, as pan depths may vary.)
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Let cool before serving.