Peach Upside Down Cake

• ¼ pound/114 grams unsalted butter, softened, plus more for greasing the pan
• 3 large, ripe peaches
• 1 ¼ cup/250 grams sugar
• 1 cup/128 grams flour
• ¾ teaspoon baking powder
• ¼ teaspoon ground nutmeg
• 3 eggs
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