Put the prawns in a bowl, cover with the anchovy juice and set aside for 30 minutes to marinate. Dry the prawns on paper towel and cut each prawn into 6 pieces.
Put a heavy-based saucepan over medium–high heat and heat the vegetable oil to 180°C (350°F) or until a cube of bread dropped into the oil turns brown in 15 seconds. Add the prawn pieces and fry for 4 minutes until golden brown (be careful as the hot oil will spit). Dry on paper towel. Cool the cooked prawns in the refrigerator for 30 minutes. Once cool, blend the cooked prawn pieces in a spice grinder until the fibres break up and the prawns take on a breadcrumb consistency. Set aside.
When ready to serve, brush each carrot with the yoghurt, making sure the carrots are evenly coated, then coat the carrots in the prawn floss and serve.
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