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FOR THE BOMBE:.
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Spread vanilla ice cream in an even layer on bottom and up sides of a 5-quart heatproof bowl with a 9 1/2 inch diameter rim.
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Ice cream should for a concave layer that comes up to the rim of the bowl.
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Freeze until set, about 20 minutes.
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Using an offset spatula, smooth the surface of the ice cream layer.
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Freeze again until very firm, at least an hour.
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Meanwhile, place chocolate and banana in a heat proof bowl., Heat cream in a saucepan until bubbles begin to form around edges.
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Pour over chocolate and banana, and let stand for 1 mintues.
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Whisk until combined.
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Set bowl over a pot of simmering water, and whisk until chololate melts.
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Refrigerate, stirring occasionally, until thickened and spreadable, about 1 hour.
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Spread chocolate-banana mixture in a thin even layer over entire surface of vanilla ice cream layer.
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Freeze until firm, about 30 minutes.
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Spread pistachio ice cream in a flat smooth layer over chololate-banana mixture, but not up sides.
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Freeze until firm, about 30 minutes.
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Spread chocolate ice cream in a flat, smooth layer over pistachio ice cream.
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Freeze until firm, about 30 minutes.
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Place banana cake over chocolate ice cream, top side up, and press gently until cake fits snugly against ice cream.
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(If vanilla ice cream and ganache layers extend beyond top of cake trim them with a sharp knife).
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Cover with plastic wrap, and freeze overnight, or up to 3 days.
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To unmold the bombe, dip bowl, in a larger bowl or very hot water or use a small kitchen torch to warm outside of bowl.
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Continue dipping or torching bowl until bombe releases when inverted onto a serving platter.
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Remove bowl, wipe ice cream drips off platter, and freeze until bombe is very firm, about 1 hour.
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MAKE THE BANANA CAKE:.
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Preheat oven to 350F Butter a 9-inch round cake pan, line with parchment cut to fit, and butter and flour parchement.
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Sift flour, baking soda, baking powder, salt, cinnamon, and a pinch of cloves into a medium bowl.
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Whisk mashed banana, buttermilk and vanilla in a small bowl.
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Beat butter and sugar, with a mixer on medium speed, until smooth.
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Add egg and beat until well combined.
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Reduce speed to low, and add flour mixture in 2 additions with banana mixture.
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Add chopped banana, and beat until well combined.
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Pour batter into pan and use a spatula to spread batter into an even layer.
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Bake until golden brown and a tester comes about 20 minutes.
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Let cake cool in pan on a wire rack for 10 minutes.
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Run a knife around edge of pan, and invert pan onto rack.
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Remove parchment and flip cake so top side faces up.
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Let cool completely on wire rack.
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FOR THE TOPPING;
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Place chocolate and shortening in a heatproof bowl set over a pot of simmering water.
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Stir until chocolate and shortening melt.
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let cool slightly, then slowly pour on top of bombe, spiraling in concentric circles to create a solid center with long drips down the sides.
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Sprinkle pistachios on top, and freeze until chocolate is set about 10 minutes.
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Run a large knife under hot water, and dry well.
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Use it to slice the bombe into sedges, as you would a cake, wiping knife between cuts.
