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1
Preheat the oven to 200u00b0 F, or the lowest possible setting. Line a baking sheet with parchment paper and set aside.
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2
In a medium bowl, combine the sugar and salt. Add the olive oil and then add enough water to turn it into a wet, sandy slurry. Toss the peeled tomatoes in the slurry until they're coated.
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3
Take the tomatoes out of the sugary oil and scatter them on a baking sheet lined with parchment paper. Bake for 2 hours, until the tomatoes are shriveled but not dry. They should be sweet and candy-like.
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4
Allow the tomatoes to cool and put them in a plastic container. Cover them completely with oil and store in the fridge. Bring to room temperature before serving.
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5
Preheat the oven to 325u00b0 F and line a quarter-sized sheet pan with parchment paper.
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6
In a stand mixer fitted with a paddle attachment, cream together the butter, sugar, and cream cheese until light, fluffy, and smooth. Add the eggs and mix until fully combined.
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7
In a separate bowl, whisk together the flour, cheese, salt, and baking powder.
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8
Add the dry ingredients to the egg and butter mixture and mix until just combined. Stream in the heavy cream, mixing until you have a smooth batter.
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9
Pour the batter into the sheet pan, tipping the pan so the batter is evenly distributed. Bake until puffed and golden, 20 to 25 minutes.
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10
Cool slightly before serving (the cake will collapse a bit). Slice into squares and top with a couple of room temperature tomatoes in their oil along with a few sprinkles of turbinado sugar. The cake is best warm; re-warm it if serving the next day.
