Bring a large pot of well-salted water to a boil. Peel the parsnips and carrots and cut them into 7½cm batons. Keep them separately. Simmer the parsnips for 10 minutes, or until cooked through but still firm. Scoop them from the water with a wire skimmer and spread on a baking sheet to cool. Simmer the carrots in the same water for 8 minutes, or until cooked through but still firm. Drain and spread on a baking sheet to cool.
Set a heavy wide-bottomed pot over a medium-high heat and melt the butter. Add the onion and cook until softened and beginning to colour, 5-8 minutes. Season with salt and add the cumin and cayenne. Add the parsnips and carrots and cook, uncovered, stirring every few minutes with a wooden spoon, allowing them to brown here and there, until fork tender, about 10 minutes. Transfer to a serving dish. Roughly chop the fresh coriander, both leaves and tender stems, to scatter over the top.