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In a chimney, light up 24 briquettes.
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Place a 10-inch Dutch oven over all the coals and melt butter. When bubbling, stir in the brown sugar and cook until dissolved.
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Spread the sugar evenly across the bottom of the pot, arrange the orange slices over the brown sugar into your desired pattern, and remove the pot from the heat.
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In a medium-size bowl, whisk together all-purpose flour, baking powder, spices, and salt.
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In a larger bowl, whisk together sugar, yogurt, orange juice, orange zest, extra virgin olive oil, and eggs until combined.
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In batches, mix the flour mixture into the yogurt mixture and stir until combined. Pour the cake batter evenly over the orange slices in your Dutch oven.
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Cover the pot and place 9 coals underneath the Dutch oven and 15 coals on top, and bake for 30 minutes or until a toothpick inserted into the center of the cake comes out clean.
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Allow the cake to cool for 10 minutes in the pot.
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Run a knife blade along the sides of the cake to ensure a clean removal.
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Place a serving plate over the Dutch oven and very carefully invert the cake.
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Remove the Dutch oven and allow cake to cool to room temperature, about 30 more minutes before serving.