Rinse the parsnips in warm water, thoroughly pat dry on a towel. Fill a pot to 1/2 with oil and heat it to 160°C. Pre-fry the parsnips in batches for approx. 5 mins. per batch; the parsnips must not take on any colour. Remove with a slotted spoon, drain on a rack lined with paper towels, leave to cool.
Heat the oil to 180°C, fry the pre-fried parsnip fries in batches with the garlic and herbs for approx. 3 mins. per batch until crispy and golden. Remove with a slotted spoon, drain on a rack lined with fresh paper towels, season with salt.
Combine the single cream and mustard, season with salt. Serve the dip with the parsnip fries.