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1
Preheat oven to 350u00b0F. Butter and flour two 9-inch-diameter cake pans with 1 1/2-inch-high sides. Sift flour, baking powder, and sea salt into medium bowl. Beat butter and 1 cup sugar in large bowl until well blended. Add 2 eggs; beat until blended. Add dry ingredients to butter mixture in 4 additions alternately with buttermilk in 3 additions. Beat remaining 4 eggs and remaining 1 1/2 cups sugar in medium bowl until mixture is thick and pale in color, about 4 minutes. Fold egg mixture into batter. Fold in bananas. Divide batter between prepared pans (about 3 1/2 cups for each).
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2
Bake cakes until tester inserted into center comes out clean, about 35 minutes. Transfer to rack; cool 15 minutes. Invert cakes onto racks; cool completely. (Can be made 1 day ahead. Wrap in foil; store at room temperature.)
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3
Combine brown sugar, banana, and 3 tablespoons butter in processor; blend until smooth. Add 1 1/2 cups whipping cream; blend. Transfer to heavy medium saucepan. Whisk over medium heat until sugar dissolves and mixture boils. Attach candy thermometer to inside of pan; cook without stirring or swirling pan until temperature registers 218u00b0F, about 10 minutes. Pour caramel into bowl. Cool to room temperature, whisking occasionally.
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4
Whisk remaining 2 1/4 cups whipping cream in large bowl until cream mounds softly. Gradually fold in cool caramel mixture. Chill until cream is firm enough to spread, about 3 hours.
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5
Cut each cake horizontally into 2 layers. Place 1 layer, cut side up, on platter. Drizzle 1 1/2 teaspoons lime juice and 1 1/2 teaspoons rum over. Spread 1 1/4 cups banana cream over. Top with second cake layer. Drizzle 1 1/2 teaspoons lime juice and 1 1/2 teaspoons rum over. Spread 1 1/2 cups cream over. Repeat with third cake layer, lime juice, rum, and cream. Top with fourth cake layer, cut side down; spread remaining cream over top.
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6
Scatter roasted pecans over top of cake. (Can be made 1 day ahead. Cover with cake dome and refrigerate.)
