Make the spice mix. Dry-fry the hazelnuts and seeds in a small, heavy-based frying pan over a medium heat for 2–3 minutes until they emit a nutty aroma. Using a pestle and mortar, pound the nuts and seeds to a coarse powder, or tip into a spice grinder and grind to a fine powder. Stir in the mint and season well. Set aside.
Pour enough oil for deep-frying into a deep saucepan and heat to 180–190°C (350–375°F), or until a cube of bread browns in 30 seconds. Deep-fry the parsnips in batches until lightly golden. Remove with a slotted spoon and drain on kitchen paper, then tip all the parsnips into a bowl while hot, and sprinkle over half the dukkah spice mix.
Reduce the heat (the beetroot slices burn easily) and deep-fry the beetroot in batches. Remove and drain as above, then tip into a bowl and sprinkle with the remaining spice mix. Serve the parsnip and beetroot crisps separately, or mixed together.