Pour the stout into a medium saucepan and heat to boiling. Reduce heat to a rapid simmer and cook until the stout is reduced by half.
Stir in the brown sugar and vanilla. Heat to boiling, reduce heat to a rapid simmer and let the mixture cook 8-10 minutes without stirring until sauce turns a deep amber and bubbles start to grow and expand. Mixture will be hot like lava, so be careful.
Remove from heat and add the butter, cream and salt and stir carefully until fully combined. Transfer to a resealable glass storage jar and let the mixture cool to room temperature. Keep in the refrigerator for up to two weeks.