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Cook pie shell as per package instructions and set aside to cool.
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Meanwhile, whisk together sugar, egg yolks, and whole egg in a large bowl until well combined. Whisk in cornstarch (until all lumps have disappeared).
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In a medium saucepan, bring the milk to a low simmer over medium heat. Slowly pour the milk into the egg mixture (fine slow stream down the side of the bowl), while whisking constantly. Whisk in vanilla, lime juice, and lime zest.
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Return mixture to pan and cook over medium heat, while whisking constantly. Cook until mixture has thicken and boils for 3-5 minutes*. Pour the custard into a bowl and cover with plastic wrap, pressing the plastic wrap directly onto the surface to prevent a skin from forming. Let cool and then refrigerate until cold, 3 hours to overnight (I only did 2 hours and placed it directly from stove to fridge as I was pressed for time).
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Right before assembling tart, place red currant jelly and 1 tbsp of water over medium-low heat. Cook until melted and smooth while stirring occasionally. Remove from heat and set aside to cool slightly.
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To assemble tart, place lime custard in pie shell and top with strawberries. Using a pastry brush, brush strawberries and tart shell with the red currant glaze. Serve immediately or refrigerate for up to 4 hours.