Heat milk and granulated sugar to about 110ºF (about 20 seconds in microwave on high). Pour into bowl of standing mixer and sprinkle with yeast. Let stand several minutes until yeast is frothy. Add flour and salt; beat to combine. Beat in egg and melted butter. Turn out onto a clean work surface and knead for a few minutes, then return dough to ball and let it rest for 30 minutes.
Preheat oven to 400ºF. Butter a 9"x2" pie dish, then press dough into the bottom and up the sides. Prick crust several times with a fork. Sprinkle bottom evenly with the brown sugar.
In a medium bowl, whisk together remaining filling ingredients. Pour over crust and bake 25-30 minutes, until filling is set and browning. Cover crust with foil or a pie protector if it is getting dark. Cool pie at least 30 minutes on a wire rack before serving. May be served warm or room temperature, with whipped cream if desired.