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Soak figs in water for 1 hour. Transfer mixture to a small saucepan and cook over medium heat until thick and stew-like, 30 minutes or longer. Remove from the heat and set aside to cool.
Meanwhile, cream sugar and butter in a large bowl with an electric mixer. Beat in milk and vanilla until smooth. Combine flour, baking powder, and salt in another bowl; stir into creamed mixture. Cover and refrigerate for 1 hour.
Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9×13-inch baking pan.
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