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Fill a large bowl with ice water and place in the fridge while you prepare the pastry cream.
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Combine the cornstarch, flour, 1/2 cup of the granulated sugar, and salt in a medium mixing bowl. Stir to combine. Place the eggs in a second medium mixing bowl and whisk until smooth. Whisk in the flour-cornstarch mixture until well combined.
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Combine the milk and remaining 1/2 cup sugar in a medium saucepan. Place pan over medium-high heat and heat to just under a boil, whisking to dissolve the sugar. Remove from the heat and, whisking the eggs constantly, very slowly pour hot milk into the egg-flour mixture.
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Transfer the mixture to a clean saucepan set over medium heat. Bring to a boil, whisking constantly, until mixture has thickened—this will take about 3 minutes.
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Transfer to a large heat-proof mixing bowl and whisk in the butter and vanilla. Whisk vigorously for 30 seconds to release some of the heat. Remove the bowl of ice water from the fridge and set the heat-proof bowl on top of the ice water. Allow the pastry cream to cool, stirring often, until completely chilled, about 10 to 15 minutes. Cover with plastic wrap, pressing wrap directly onto the surface of the pastry cream. Refrigerate until ready to use.
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Once tart shell is completely cool, place the heavy cream in the bowl of a stand mixer fitted with the whisk attachment. Whip until soft peaks form, then gently fold into the pastry cream. Gently spread the pastry cream into the bottom of the tart shell in an even layer. (If you have filling left over, store it in the fridge—it makes a delicious dip for fruit.)