In a medium saucepan, combine the brown sugar, cornstarch, and salt. Whisk together until well blended.
Gradually add the whole milk to the dry ingredients, whisking continuously to prevent lumps.
Place the saucepan over medium heat and cook, stirring constantly, until the mixture thickens and begins to bubble, about 5-7 minutes.
Remove the saucepan from heat and stir in the butter and vanilla extract until fully melted and combined.
In a separate bowl, mix the hot water with the remaining brown sugar until dissolved.
Pour the butterscotch pudding into a serving dish or individual ramekins. Carefully pour the hot water mixture over the pudding.
If desired, sprinkle chopped pecans on top.
Let the pudding sit for about 10 minutes before serving to allow the sauce to form.