In the top of a double boiler, heat milk over high heat until just before boiling, stirring often with a whisk. While milk warms, combine 1 cup brown sugar, flour, and salt in a medium bowl. Once milk is hot, add sugar mixture, reduce heat to medium-high, and stir slowly and regularly with whisk until sugar is dissolved and mixture thickens, about 15 to 20 minutes.
Off the heat, add eggs and cook for 2 more minutes, stirring constantly. Then add 1 tablespoon of butter and the vanilla. Cook until the consistency of the butterscotch filling is just a touch thinner than a pudding.
Pour butterscotch into prepared pie crust.
Prepare topping by melting remaining 1 tablespoon of butter and combining it with remaining 2 tablespoons of brown sugar and the pecans. Garnish pie with pecans and allow it to set up about 30 minutes to an hour to serve warm to room temperature. Or, chill the pie in the refrigerator for an hour or more and serve cool.