Butter a rimmed baking sheet; set aside.
Mix sugar and cream together in a large heavy-bottomed saucepan. Place over medium-low heat and bring to a boil. Add butter, and cook, without stirring, until mixture reaches 240 degrees on a candy thermometer, 50 to 60 minutes.
Pour mixture onto prepared baking sheet in an even layer. Let cool 2 hours. Transfer mixture to a large bowl and stir in vanilla. Using your hands, begin to pull and press the mixture. Keep pulling and kneading mixture until it lightens in color, loses its shine, and no longer sticks to your fingers, 15 to 45 minutes. Roll mixture into small balls, about 1 inch in diameter. Place on a parchment-paper-lined baking sheet and refrigerate until firm and cold, about 10 minutes.
In a heatproof bowl set over (but not touching) simmering water, melt chocolate and food paraffin, stirring until smooth and well combined. Using a toothpick, dip each ball into chocolate mixture, and return to baking sheet. Refrigerate until fudge is chilled and chocolate has set, about 30 minutes. Bring to room temperature before serving.
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