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1
Toss strawberries with brown sugar in a bowl and let stand while you complete remaining steps, about 30 minutes.
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2
Preheat oven to 350 degrees F (175 degrees C).
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3
Whisk flour, 1 tablespoon white sugar, and 1/4 teaspoon salt in a bowl until thoroughly combined. Cut butter into the flour mixture until it resembles coarse crumbs, and drizzle in milk. Mix just until the dough holds together. Turn dough out onto a floured surface and roll out into a 10-inch circle. Fit dough into a 9-inch pie dish. Prick the dough several times on the bottom and sides; fill with dry beans or pie weights.
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4
Bake the crust in the preheated oven until golden brown, about 25 minutes. Remove crust and let cool.
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5
Bring cream just barely to a simmer in a saucepan over low heat. Whisk egg yolks thoroughly in a bowl with 1/4 teaspoon salt and add about 1 tablespoon of the hot cream to the beaten yolks, whisking constantly. Continue to add and whisk hot cream into the yolks until about 2/3 cup of cream has been added, then whisk the yolk mixture into the remaining hot cream in the saucepan, pouring it in a thin stream. Continue whisking until cream mixture is thick and smooth, about 5 more minutes; do not let boil or custard will curdle. Remove custard from heat and let stand until it reaches room temperature, about 30 minutes.
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6
Drain juice from strawberries and layer them into the bottom of the baked pie shell. Spread cream custard over the berries; refrigerate until set, about 4 hours.
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7
Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
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8
Sprinkle 1/4 cup white sugar evenly over top of pie and broil until the sugar is browned, about 5 minutes. Let pie stand 5 minutes for sugar topping to cool before serving.
