In heavy saucepan, heat butter, brown sugar, and salt to boiling, stirring frequently. Remove from heat; set aside.
In small bowl, stir cornstarch into 1/3 cup of the milk until dissolved. Add egg yolks; beat with whisk until blended.
Into saucepan with brown sugar mixture, pour remaining 2 cups milk, heavy cream and stir to combine. Add the cornstarch mixture. Heat to boiling over medium heat, stirring constantly. When pudding comes to a rolling boil, remove from heat. Allow to cool for 5 minutes.
Pour pudding into prepared pie shell. Refrigerate for 3 hours.