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1
Preheat the oven to 350F (175C).
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2
To make the crust, generously butter a 10-inch (25-cm) pie plate.
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3
In a medium bowl, mix together the chocolate cookie crumbs, the 3 tablespoons (45 g) sugar, and 4 tablespoons (2 ounces/60 g) melted butter until evenly moistened.
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4
Pat the mixture in an even layer into the bottom and up the sides of the buttered pie plate.
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5
Refrigerate or freeze for 30 minutes.
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6
Bake the crust until if feels slightly firm, about 10 minutes.
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7
Let cool completely.
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8
To make the filling, in a small saucepan, heat the brown sugar and the 2 tablespoons (1 ounce/30 g) butter, stirring, until the butter is melted.
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9
Pour into a large bowl, set a mesh strainer across the top, and set aside.
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10
In a small bowl, whisk the cornstarch with just enough of the milk to make a smooth slurry.
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11
In a medium saucepan over medium heat, warm the remaining milk and the salt.
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12
When the milk is hot, stir the cornstarch mixture to recombine, then whisk it into the milk in the saucepan.
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13
Cook over medium heat, stirring constantly, until the mixture begins to boil and thickens.
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14
Whisk the egg yolks in a small bowl, then whisk a small amount of the hot thickened milk mixture into the yolks.
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15
Whisk the warmed egg-yolk mixture into the saucepan.
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16
Cook, stirring constantly, until the mixture returns to a boil and is as thick as mayonnaise.
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17
Pour it through the strainer into the butterbrown sugar mixture.
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18
Add the 2 teaspoons rum and 1/2 teaspoon vanilla and whisk until combined.
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19
Peel and cut the bananas into slices 1/4 inch (6 mm) thick and scatter them in the bottom of the cooled crust.
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20
Pour the filling into the crust, cover with plastic wrap, and refrigerate until chilled, about 2 hours.
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21
To make the topping, in a stand mixer fitted with the whip attachment (or in a bowl by hand), whisk the cream on high speed until it begins to mound softly.
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22
Add the 1 tablespoon sugar and 2 tablespoons rum and continue whisking until the cream holds peaks.
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23
Spread or pipe the topping over the pie.
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24
Garnish with chocolate curls.
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25
The baked or unbaked crust can be refrigerated for up to 4 days, or frozen for up to 1 month.
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26
The pie can be refrigerated for up to 2 days, but whip the cream and top the pie with it a few hours before serving.
