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In a bowl, beat the sugar into the eggs until thickened and pale yellow; beat in the flour and salt; set aside.
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Bring milk to a boil in a pan; slowly beat the hot milk into the egg/sugar mixture.
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Pour the entire mixture back into the pan and place over low heat.
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Stir constantly with a whisk or wooden spoon until the custard thickens slightly; be careful not to let the mixture boil or the eggs will scramble.
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Remove pan from heat and pour hot custard through a strainer into a large, clean bowl.
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Mash the bananas with a fork until they are creamy (or puree them in a food processor).
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Add the banana puree to the hot custard; mix well.
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Allow the banana custard to cool slightly; stir in the cream, vanilla, and liqueur.
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Cover and refrigerate until cold or overnight.
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Stir the chilled custard, then freeze in 1 or 2 batches in your ice cream maker according to manufacturer’s directions.
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When finished, the ice cream should be soft but ready to eat; for firmer ice cream, transfer to a freezer-safe container and freeze several hours or overnight.