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1
In a medium-size skillet over medium heat, melt 3 tablespoons of the butter.
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2
Add the sugar and stir until it dissolves.
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3
Add the bananas and cook, stirring, for 3 minutes.
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4
Remove the pan from the stove and carefully add the liqueur and rum.
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5
Return the pan to the stove.
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6
Using long matches and keeping long hair and hanging sleeves well clear of the pan, carefully ignite the alcohol and stir with a long-handled wooden spoon until the flames die down, about 30 seconds.
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7
Remove from the heat and let cool completely.
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8
Puree the mixture in a food processor or blender.
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9
In a medium-size nonreactive saucepan over medium heat, heat the milk and cream to the scalding point (when bubbles form around the edges of the pan).
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10
Do not let it boil.
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11
Remove from the heat.
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12
Beat the egg yolks in a large mixing bowl.
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13
Add the cream mixture about 1/4 cup at a time to the beaten eggs, whisking well after each addition.
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14
Pour the mixture back into the saucepan, and cook, stirring, over medium heat until the custard becomes thick enough to lightly coat the back of a spoon, 2 to 3 minutes.
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15
Do not boil.
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16
Remove from the heat and pour the mixture into a large glass mixing bowl.
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17
Add the pureed bananas and stir to mix.
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18
Cover the top of the mixture with plastic wrap pressed against the surface (this will keep a skin from forming) and let cool.
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19
Place the mixture in the refrigerator and chill completely.
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20
Pour the banana mixture into an ice cream machine and follow the manufacturers instructions for the churning time.
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21
If you leave the ice cream in the freezer for a while before completing the pie, be sure to let it soften up a bit first.
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22
Make caramel sauce: In a small heavy saucepan, combine the sugar and water and bring to a boil, stirring often.
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23
Cook, stirring occasionally, until the mixture is a deep caramel color and has the consistency of thick syrup, 10 to 15 minutes.
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24
Remove from the heat.
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25
Stir in the cream, return the saucepan to high heat, and boil the sauce until it regains the consistency of a thick syrup, about 2 minutes.
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26
Let cool.
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27
The sauce can be refrigerated until ready to use.
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28
Allow it to reach room temperature before using it.
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29
Preheat the oven to 375 degrees F.
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30
Put the graham cracker crumbs in a medium-size mixing bowl.
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31
Melt the remaining 5 tablespoons butter and add to the crumbs.
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32
Mix well.
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33
Press evenly into the sides and bottom of a 9 1/2-inch deep-dish pie pan and bake until browned, about 10 minutes.
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34
Let cool completely.
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35
Carefully spread the caramel sauce evenly over the inside of the graham cracker shell.
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36
Fill the shell with the ice cream, spreading it evenly with a rubber spatula.
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37
Cover with plastic wrap and freeze until the ice cream firms up, about 4 hours.
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38
Cut the pie into wedges to serve.
