In a medium saucepan, combine the sugar, water, and cream of tartar. Stir gently over medium heat until the sugar dissolves.
Once dissolved, stop stirring and let the mixture come to a boil. Use a candy thermometer if possible; it should reach 149–154°C (300–310°F), the hard-crack stage.
Remove the saucepan from the heat. Stir in the vanilla essence and a few drops of food colouring if you want coloured cotton candy.
Using wooden sticks or paper cones, spin the sugar quickly in thin threads by dipping the stick into the syrup and letting the sugar thread off in fine strands. You can do this over a greased surface or use a fork to wrap the threads around the stick. Be careful, as the syrup is extremely hot.
Shape the sugar threads into fluffy cotton candy balls or cones. Serve immediately for best texture.