Combine the butter and half and half in a double boiler or a saucepan that you've set over another larger pot with simmering water. Warm until the butter is melted. Whisk together.
4 tablespoons butter, 1 cup half & half
Add the chocolate, espresso, brown sugar, vanilla, and sea salt to the mixture and bring to a simmer; whisking continuously until smooth.
6 ounces semi-sweet , 6 ounces milk chocolate, 1 teaspoon espresso, 1/2 cup brown sugar, 1 tablespoon vanilla extract, 1/8 teaspoon sea salt
Use an immersion blender (or pour mixture into a countertop blender) and blend until smooth and shiny.
Cool slightly before serving warm over your favorite ice cream.
Refrigerate to store; heat in warm water or microwave on low power before using.
Notes
Mexican Hot Fudge Sauce
Add 1/4 cup of tequila to milk and butter and boil for one minute to boil off alcohol. Add an additional 1/2 teaspoon of espresso powder, 1/2 to 1 teaspoon cayenne pepper and 1 teaspoon cinnamon to sauce when you add the rest of the ingredients. Mix well. I like to serve a sundae with this sauce and crumbled up cinnamon tortillas.