1. Combine the flour, sugar, yeast, and salt in a large bowl Stir to combine. Make a well in the center and add the milk, eggs, and butter. Stir the batter together until it is well combined and cohesive. The batter will look somewhere between a loose bread dough and a thick cake batter. Cover the bowl with plastic wrap and let it rise in a draft-free spot for an hour. The mixture will not quite double in size.
2. Butter a 9x13-inch baking dish and line it with parchment paper. Stir the batter a few times to deflate it slightly, then scrape it into the prepared pan and spread it until it more or less fills the bottom of the pan. Cover again with plastic wrap and set aside for another 30 minutes. While the cake is rising again preheat the oven to 350° F.
3. Once the cake has risen, gently place the fig quarters into the top of the batter.
4. Bake the cake for 25-30 minutes, until top is golden and a toothpick inserted into the center comes out clean. Transfer to a cooling rack and let it sit in the pan for 10 minutes. After 10 minutes, run a knife along the outside of the cake and invert it onto a cooling rack. Invert it back onto another rack to cool completely.
5. Serve sliced into squares, plain or with whipped cream
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