Toss strawberries with brown sugar and let stand about 30 minutes.

Preheat oven to 350°F (175°C).

Whisk flour, white sugar, and salt in a bowl. Cut butter into the mixture until coarse crumbs form. Add milk and mix until dough holds together.

Roll out dough into a 10-inch circle and fit into a 9-inch pie dish. Prick the bottom and sides, then fill with dry beans or pie weights.

Bake crust in preheated oven until golden brown, about 25 minutes. Remove and let cool.

Heat cream in a saucepan until it just starts to simmer. Slowly whisk hot cream into egg yolks. Return to pan and heat cream mixture until thick and smooth, about 5 minutes. Let cool to room temperature.

Drain juice from strawberries and layer them into the pie shell. Spread cream custard on top and refrigerate until set, about 4 hours.

Preheat oven's broiler and sprinkle white sugar evenly over the pie. Broil until sugar is browned, about 5 minutes.