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1. FOR THE FILLING: Sprinkle gelatin over water in large bowl and set aside. Whisk egg yolks and cornstarch together in medium bowl until combined. Combine raspberries, sugar, butter, and salt in medium saucepan. Mash lightly with whisk and stir until no dry sugar remains. Cook over medium heat, whisking frequently, until mixture is simmering and raspberries are almost completely broken down, 4 to 6 minutes.
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2. Remove raspberry mixture from heat and, whisking constantly, slowly add 1/2 cup raspberry mixture to yolk mixture to temper. Whisking constantly, return tempered yolk mixture to mixture in saucepan. Return saucepan to medium heat and cook, whisking constantly, until mixture thickens and bubbles, about 1 minute. Pour through fine-mesh strainer set over gelatin mixture and press on solids with back of ladle or rubber spatula until only seeds remain. Discard seeds and stir raspberry mixture until gelatin is dissolved. Set aside, stirring occasionally, until curd is slightly thickened and reaches room temperature, at least 30 minutes or up to 1 hour 15 minutes.
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3. FOR THE JAM MIXTURE: Sprinkle gelatin over lemon juice in small bowl and let sit until gelatin softens, about 5 minutes. Heat jam in microwave, whisking occasionally, until hot and fluid, 30 to 60 seconds. Add softened gelatin to jam and whisk until dissolved. Set aside.
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4. FOR THE CAKE: Adjust oven rack to upper-middle position and heat oven to 350 degrees. Lightly grease 8-inch round cake pan and 8-inch square baking pan, line with parchment paper, and lightly grease parchment. Whisk flour, sugar, baking powder, and salt together in medium bowl. Whisk oil, whole egg, water, and vanilla into flour mixture until smooth batter forms.
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5. Using stand mixer fitted with whisk, whip egg whites and cream of tartar on medium-low speed until foamy, about 1 minute. Increase speed to medium-high and whip until soft peaks form, 2 to 3 minutes. Transfer one-third of egg whites to batter; whisk gently until mixture is lightened. Using rubber spatula, gently fold remaining egg whites into batter.
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6. Pour 1 cup batter into round pan and spread evenly. Pour remaining batter into square pan and spread evenly. Place pans on rimmed baking sheet and bake until cakes spring back when pressed lightly in center and surface is no longer sticky, 8 to 11 minutes (round cake, which is shallower, will be done before square cake). Cakes should not brown.
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7. Let cakes cool in pans on wire rack for 5 minutes. Invert round cake onto wire rack. Carefully remove parchment, then reinvert onto second wire rack. Repeat with square cake. Let cool completely, at least 15 minutes.
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8. Place round cake in center of serving platter. Spread with 2 tablespoons jam mixture. Place ring from 9-inch springform pan around cake, leaving equal space on all sides. Leave clasp of ring slightly loose. Using sharp chef's knife, trim 1/8 inch off all edges of square cake. Spread square cake with 2 tablespoons jam mixture. Cut cake in half. Cut each half lengthwise into two pieces to make four equal-size long strips. Place cake strips vertically around round cake, jam side in, taking care to nestle ends together neatly. Fasten clasp of springform ring.
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9. Using stand mixer fitted with whisk, whip cream on medium-low speed until foamy, about 1 minute. Increase speed to high and whip until soft peaks form, 1 to 2 minutes. Transfer one-third of whipped cream to curd; whisk gently until mixture is lightened. Using rubber spatula, gently fold in remaining cream until mixture is homogenous.
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10. Pour filling into cake ring and spread evenly to edge. (Surface of filling will be above edge of cake.) Drizzle remaining jam mixture over surface of filling. Using knife, swirl jam through surface of filling, making marbled pattern. Refrigerate for at least 5 hours or up to 24 hours.
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11. To unmold, run thin knife around edge of ring (just 1/2 inch down). Release ring and lift to remove. Let stand at room temperature for 20 minutes before slicing and serving.
