Microwave 1/2 cup butter in a heatproof bowl to melt. Add chocolate, stirring until melted, then add sugar and cocoa and stir to blend. Whisk in eggs, vanilla, and salt. Add flour and stir until smooth. Spoon batter evenly into muffin cups.
Using a small spoon, make a depression in each portion of batter 1 in. wide and 1/2 in. deep. Spoon 1 tbsp. chocolate hazelnut spread into each.