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1
Stir together the milk and 1 cup of cream.
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2
Dissolve the cornstarch in 1/3 cup of the cream mixture.
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3
Whisk in the egg yolk.
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4
Mix 88 grams of sugar (about 1/3 cup), 1/8 teaspoon of salt, and the remaining cream mixture in a heavy saucepan.
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5
Bring the mixture to a simmer and remove from heat.
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6
Whisk a third of the sugar-and-cream mixture into the egg yolk mixture, then stir that into the saucepan.
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7
Return to medium heat and stir without stopping, being sure to stir the bottom and sides of the pan, for 5 minutes, until the mixture thickens and coats the back of a spoon.
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8
Remove from heat and stir in 1 teaspoon vanilla extract.
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9
Strain into a bowl, cover this pudding with plastic and chill completely, at least 3 hours.
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10
Stir together the gluten-free flour, sweet rice flour, 8 grams of sugar (about 1 1/2 teaspoons) and the remaining 1/8 teaspoon of salt.
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11
Cut the butter into chunks and, using your fingertips, work the butter into the dry ingredients to form a coarse meal.
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12
Make a well.
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13
Break the egg into the well.
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14
Add the lemon juice.
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15
Use a fork to stir from the center, working the flour into the egg to form a soft dough.
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16
Shape into a disk and chill in the freezer for 15 minutes.
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17
Heat the oven to 400 degrees.
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18
Grease a pie pan and press the pastry into it in an even layer.
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19
If the dough seems very sticky, put a piece of parchment paper on top and pat it out to smooth, then remove it.
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20
Bake until golden brown, 12 to 15 minutes.
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21
Transfer to a wire rack to cool completely.
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22
To assemble the pie, pour half the pudding into the crust.
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23
Slice 2 of the bananas and arrange the slices over the pudding.
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24
Pour the remaining pudding on top of the bananas.
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25
Cover with plastic wrap and refrigerate until thoroughly cooled, about 3 hours.
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26
Just before serving, slice the remaining banana and arrange the slices over the pudding.
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27
Whip the remaining cup of cream until stiff.
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28
If you like, add confectioners sugar and remaining 2 teaspoons of vanilla extract.
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29
Spread whipped cream on top or pipe it from a pastry bag.