Melt butter in a medium saucepan. Add flour and salt and stir until smooth. Stir in brown sugar and cook over medium heat, stirring constantly, until the mixture bubbles and is lightly browned, about 5 minutes.

Remove from heat. Stir in boiling water.

Return to heat and bring to a boil, stirring constantly, until smooth and thickened. Stir in vanilla extract until well blended. Serve hot.