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Butter and line a 20cm square cake tin with baking parchment. Put the butter, condensed milk, sugar and milk in a large saucepan over a low heat. Stir continuously until the sugar dissolves.
Increase the heat and bring to the boil. Bubble for 10 mins, stirring all the time until the mixture reaches 115C on a sugar or probe thermometer. Remove from the heat and leave to cool to 110C. Add the vanilla, then beat in a stand mixer or with an electric hand whisk until it cools to 60C. This will help break up any large sugar crystals. The fudge should be thick and matte-looking.
Spoon the fudge into the prepared tin and press down with a spoon to smooth the surface. Leave to set, then cut into squares. Will keep for up to three weeks in an airtight container.