Line an 8x8-inch (20x20 cm) pan with parchment, leaving an overhang on two sides.
Put the chocolate, condensed milk and butter in a medium heavy saucepan over the lowest heat. Stir constantly with a spatula as it melts, 4–6 minutes, until completely smooth and glossy. (Microwave route: heat in a microwave-safe bowl in 30-second bursts, stirring well between each, until smooth.)
Take off the heat. Stir in the vanilla and salt until evenly mixed.
Scrape into the lined pan and smooth the top. Scatter the sprinkles over and press them very lightly so they stick.
Refrigerate at least 3 hours, until fully firm.
Lift out by the parchment and cut into 36 small squares with a large sharp knife (fudge is rich — small is right). Wipe the blade between cuts for clean edges.