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Preheat the oven to 350°F. Grease two 8" round cake pans that are at least 2" deep. Line with parchment and grease the parchment.
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To make the cake: Combine the milk, egg whites, vanilla, Fiori di Sicilia, and lemon zest in a large measuring cup; set aside.
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In the bowl of a stand mixer fitted with a paddle, mix together the flour, granulated sugar, baking powder, and salt at low speed.
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Add the butter and mix until the mixture looks sandy.
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Add 1 cup of the milk/egg mixture and beat at medium speed for 1 1/2 minutes. Scrape the bowl and add the remaining milk mixture; beat for 30 seconds. Scrape the sides of the bowl once more and beat for another 20 seconds.
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Divide the batter evenly between the prepared pans.
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Bake until the cakes begin to pull from the sides of the pans and spring back when lightly touched in the center, about 28 to 32 minutes. Remove from the oven and place on a rack for 5 minutes. After 5 minutes, turn out of the pans and return to the rack to finish cooling completely.
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To make the frosting: Dissolve the granulated sugar in the boiling water; let cool completely.
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Put the cooled sugar syrup in a large mixing bowl, add the meringue powder and beat using a whisk attachment until soft peaks form.
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Add the confectioners' sugar, mixing until thoroughly combined.
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Add the butter and beat until creamy. Beat in the flavorings and salt.
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To make the raspberry filling: Remove 1 1/2 cups of the frosting and stir in the raspberry jam. Set aside.
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To make the lemon filling: Place the granulated sugar and Instant ClearJel in a saucepan and whisk to combine. Add the lemon zest, lemon juice, and salt.
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Add the butter and bring the mixture to a boil over medium heat. Boil for 1 minute, stirring constantly.
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Whisk in a small amount of the hot lemon mixture into the egg yolks; add the egg mixture back to the saucepan and cook, stirring, until thick (don't let it boil).
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Pour the lemon filling into a bowl and cover with plastic wrap, pressing it onto the surface to keep a skin from forming as it cools. Refrigerate until cold.
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To assemble: Cut the two cake layers in half horizontally, to make four layers.
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Put one layer of cake on a serving plate, cut side down. Frost with half the raspberry-flavored frosting, then place about 1/3 of the fresh raspberries on top. If they're very tall, slit them up the side and lay them down flat in an even layer.
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Place the second cake layer atop the first, and pipe a ring of lemon buttercream around the outside edge. Fill the circle with the lemon filling.
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Add a third layer, frosting with the remaining raspberry frosting. Place half the remaining raspberries on the frosting.
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Top with the last layer, cut side down. Frost the top and sides with the remaining lemon frosting and top with the last of the raspberries.
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Store leftover cake with plastic wrap touching the cut edges to keep the cake from drying out; keep in the refrigerator for up to 5 days.