CARAMELIZED PEACH UPSIDE-DOWN CAKE

Steps:

• Put oven rack in middle position and preheat oven to 400°F.
• Melt 2 teaspoons butter, then brush muffin cups with some of it. Chill muffin tin 2 minutes to set butter. Line bottom of each muffin cup with a round of parchment paper, then brush cups and parchment with remaining melted butter and chill 2 minutes more. Divide 1 teaspoon flour among muffin cups and shake to coat, knocking out excess flour.
• Cut an X in bottom of each peach and immerse peaches in a large pot of boiling water until skins loosen, about 15 seconds. Transfer peaches with a slotted spoon to a large bowl of ice and cold water to cool. Peel peaches, then pit and halve lengthwise. Cut peach halves lengthwise into 1/2-inch-thick slices, then cut slices crosswise into 1/2-inch pieces.
• Melt remaining tablespoon butter in a 10-inch heavy skillet over moderate heat, then stir in 3 tablespoons brown sugar and cook, stirring occasionally, until sugar is melted and bubbling, about 2 minutes. Carefully add a scant 2 cups peaches (caramel will splatter and sugar will seize), reserving remaining 1/3 cup peaches, then reduce heat and simmer, stirring occasionally, until peaches are tender and caramel is syrupy, 6 to 8 minutes. Spoon cooked peaches and caramel evenly into muffin cups.
• Purée reserved peaches in a blender until smooth. Beat together eggs, salt, almond extract, and remaining 6 tablespoons brown sugar in a bowl with an electric mixer at high speed until mixture is creamy and tripled in volume, 3 to 5 minutes in a stand mixer or 6 to 8 minutes with a handheld. Reduce speed to low, then add puréed peaches and mix until just combined. Sift remaining 6 tablespoons flour evenly over egg mixture and fold in gently but thoroughly until just combined.
• Spoon batter over caramelized peaches and bake until golden brown and a wooden pick or skewer inserted in center of a cake comes out clean, 10 to 12 minutes. Cool in muffin tin on a rack 2 to 3 minutes, then invert a platter over muffin tin and flip cakes onto platter while still warm. Reposition any peaches that have stuck to parchment and serve cakes warm or at room temperature.