To make the chips, slice the parsnips as thinly as possible into long strips or rounds using a sharp knife or mandoline cutter. Heat the oil in a large, heavy-based saucepan to 375F (190C) or until a small cube of bread turns golden in 30 seconds. Deep-fry the vegetables in small batches (a small handful at a time) for about 2 minutes each batch. As they cook the parsnips slices with curl and turn golden. Remove with a slotted spoon and drain on paper towels, sprinkling with salt while still warm.
To make the dip, Combine first five ingredients in a food processor and pulse until almost smooth. Add remaining ingredients and pulse one or two times until combined. Add more salt or pepper if needed.