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Gather all ingredients. Preheat the oven to 375 degrees F (190 degrees C). Coat a 9-inch square baking pan with cooking spray; line with parchment paper, leaving a 2-inch overhang on two sides. Spray parchment paper with cooking spray.
Photographer: Robby Lozano / Food Styling: Nicole Hopper / Prop Styling: Keoshia McGee
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Beat eggs and sugar with an electric mixer on medium speed until pale and thickened, 1 to 2 minutes. With mixer on low speed, beat in half-and-half until smooth, about 5 seconds, then beat in flour until just combined, 20 to 30 seconds.
Photographer: Robby Lozano / Food Styling: Nicole Hopper / Prop Styling: Keoshia McGee
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Peel apples and grate them using the large hole side of a box grater. Transfer grated apples to a fine-mesh strainer and drain, pressing gently down on apples, until no longer dripping. Fold grated apples into egg mixture until evenly coated.
Photographer: Robby Lozano / Food Styling: Nicole Hopper / Prop Styling: Keoshia McGee
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Spoon mixture into prepared pan and smooth top into an even layer.
Photographer: Robby Lozano / Food Styling: Nicole Hopper / Prop Styling: Keoshia McGee
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Bake in the preheated oven until a wooden pick inserted in the center comes out clean, edges are browned, and the top feels set to the touch, 35 to 40 minutes. Let cool in pan on wire rack slightly, about 20 minutes, then transfer to the refrigerator to cool completely, 1 to 2 hours.
Photographer: Robby Lozano / Food Styling: Nicole Hopper / Prop Styling: Keoshia McGee
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If needed, run a flat-edged knife along sides of pan, then lift cake from pan using parchment handles and transfer to a cutting board. Dust top with powdered sugar and slice into 2-inch squares. Serve chilled or at room temperature.
Photographer: Robby Lozano / Food Styling: Nicole Hopper / Prop Styling: Keoshia McGee
Recipe developed by Elizabeth Mervosh