Melt butter and chocolate in a small saucepan over low heat; set aside.
Combine sugars, eggs, milk, flour and vanilla in a medium bowl. Gradually add chocolate mixture, beating constantly. Pour into unbaked pie crust; bake at 325° for 40 to 45 minutes. Let cool before serving. Garnish, if desired.
Made this pie for a Thanksgiving family reunion. It was gone in minutes with some family members disappointed because they didn't get a piece. I should have made two! It didn't get 5 stars because although I baked it 45 minutes, it did not set in the middle. Even though it was not done (and fairly runny in the middle), the flavor was delicious and family members loved it! Will definitely try again and bake a little longer.