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For cake:.
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Preheat oven to 350F Butter and flour two 9-inch round cake pans with 2-inch-high sides.
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Butter two 9-inch parchment paper rounds and place in pans, buttered side up.
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Stir white chocolate in top of double boiler set over barely simmering water until melted and smooth.
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Leave white chocolate in pot; turn off heat.
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Sift flour, baking powder, and salt into medium bowl.
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Using electric mixer, beat butter and sugar in large bowl until well blended.
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Add eggs 1 at a time, beating well after each addition.
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Beat in vanilla.
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Add dry ingredients alternately with milk in 3 additions, blending well after each addition.
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Add warm white chocolate and beat just until blended.
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Divide batter equally between pans, smoothing tops with spatula.
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Bake cakes until tester inserted into centers comes out clean, about 30 minutes.
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Cool cakes in pans on racks 20 minutes (cakes will fall).
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Run small sharp knife around cake pan sides.
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Turn cakes out onto cardboard round or tart pan bottom; peel off parchment.
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Turn cakes right side up onto racks and cool completely.
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For buttercream:.
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Stir white chocolate in top of double boiler over barely simmering water until melted and smooth.
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Remove white chocolate from over water.
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Let stand until cool but not set, about 20 minutes.
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Using electric mixer, beat butter in large bowl until fluffy.
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Beat in white chocolate and vanilla, scraping down sides of bowl occasionally.
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Beat in powdered sugar.
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Cover and refrigerate until thick enough to spread, about 45 minutes (frosting will be very soft).
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For assembly:.
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Boil 1/2 cup water and sugar in small saucepan over medium heat, stirring to dissolve sugar.
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Cool syrup.
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Using serrated knife, cut each cake layer horizontally in half.
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Place 1 layer, cut side up, on 9-inch cardboard cake round or removable bottom of 9-inch tart pan and brush with 2 tablespoons sugar syrup.
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Spread 6 tablespoons buttercream over cake.
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Cover buttercream with single layer of sliced apricots.
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Spread 3 tablespoons buttercream over apricots; top with second cake layer, cut side up.
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Brush with 2 tablespoons sugar syrup, 6 tablespoons buttercream, apricots, and 3 tablespoons buttercream.
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Top with third cake layer, cut side up.
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Brush with 2 tablespoons syrup.
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Spread 6 tablespoons buttercream over cake; cover with apricots.
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Spread 3 tablespoons buttercream over apricots.
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Top with fourth layer, cut side down.
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Spread 1 cup buttercream over top and sides of cake (layer will be thin).
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Chill 1 hour.
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Spread remaining buttercream over top and sides of cake.
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Press chopped walnuts onto sides of cake.
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Cover top with remaining sliced apricots.
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Brush apricots with apricot preserves.
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Chill cake 1 hour.
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(Can be made 1 day ahead.
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Cover with cake dome and keep chilled.
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Let stand 3 hours at room temperature before serving.
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50
).
