Cook the parsnips in a large saucepan of lightly salted boiling water for 10 minutes until tender.
Meanwhile, melt the butter in a small frying pan, add the garlic and thyme and cook gently, stirring, for 2 minutes.
Drain the parsnips, return to the pan and mash thoroughly. Mash in the buttery garlic mixture and season well with salt and pepper. Leave until cool enough to handle.
Shape the parsnip mixture into 8 patties with lightly floured hands.
Heat 1 tablespoon of the oil in a large frying pan, add 4 of the patties and cook for 3–4 minutes on each side until golden brown. Transfer the patties to a baking sheet and keep warm in a low oven while you repeat with the remaining oil and patties. Serve warm.