Grease an 8-inch square baking pan.

Put the sugar and cocoa in a medium saucepan and stir in the milk until smooth. Heat over medium-high, stirring all the time, until it comes to a boil.

Turn the heat to low and clip a candy thermometer to the pan. Let it simmer without stirring until it reaches 238°F (114°C), about 10 minutes.

No thermometer? Drop a little of the mixture into cold water. When it forms a soft ball that flattens once you take it out and set it down, it is ready.

Take the pan off the heat and leave it alone to cool to 110°F (43°C), 50 to 70 minutes. Do not stir or move it while it cools.

Add the butter and vanilla, then beat with a wooden spoon until fully mixed in and the fudge turns from glossy to matte. Keep going until the shine is gone.

Pour into the prepared pan and press it flat. Let it cool completely, at room temperature or in the fridge, then cut into 1-inch squares.