In a small saucepan, combine the melted butter, brown sugar and vanilla extract.
Bring to a slow boil until foamy; add the sweetened condensed milk.
Bring back to a slow boil, over medium low heat and cook, stirring continuously, for another 3 or 4 minutes or until the mixture darkens slightly.
Remove from heat and pour into the prepared crust.
Place in refrigerator and chill for 2 hours or more until thoroughly cooled.