For rum sauce: Melt butter in heavy medium saucepan over medium-high heat. Add cream, sugar, and salt. Bring to a boil, stirring until sugar dissolves. Remove from heat. Stir in rum. (Can be prepared 2 days ahead.
Cover and refrigerate. Rewarm over low heat, stirring constantly.)
For Banana Bread Pudding: Combine raisins and 2 tablespoons rum in a small bowl. Let stand 20 minutes. Melt 2 tablespoons butter in a heavy skillet over medium heat. Add banana and 2 tablespoons sugar and cook until bananas are tender, about 2 minutes per side. Remove from heat. Combine whipping cream, eggs, vanilla extract and remaining 1/4 cup rum and 3 tablespoons sugar in medium bowl and whisk to blend. Preheat oven to 350'F. Butter 9x5x3-inch loaf pan. Arrange 1/3 of bread strips crosswise in bottom of prepared pan. Arrange 6 banana pieces atop bread. Sprinkle with half of raisins and half of pecans. Arrange 1/3 of bread strips crosswise atop bananas. Pour half of egg mixture over.
Arrange remaining banana pieces atop bread. Sprinkle remaining pecans and raisins. Arrange remaining bread strips crosswise atop bananas. Pour remaining egg mixture over. Press gently on top layer to compact.
Let stand 15 minutes. Bake bread pudding until puffed and golden and a knife inserted into the center comes out clean, about 45 minutes. Transfer to rack and cool slightly. Cut bread pudding into slices. Arrange on plates; drizzle with warm Rum Sauce and serve. 6-8 servings
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