Method
Make the rosti. Place the grated parsnip in a bowl along with all the other ingredients, except the oil for frying. Use your hands to thoroughly combine the mixture, squeezing it through your hands as you go. Leave it to sit for 5 minutes, then mix again.
Heat your biggest non-stick frying pan over a medium heat and add a little sunflower oil. Lift a quarter of the rosti mixture out of the bowl and into the hot pan. Use a fork to arrange it quickly into a nice, flat, rustic round, no thicker than 1cm (1⁄2in) or so. If you have a large enough pan, repeat for another quarter of the mixture – and so on. (If your pan isn’t large enough, though, fry in batches.) Give each rosti about 6–8 minutes on each side, until golden and crispy all over.
Keep the rostis warm while you cook the eggs. Melt the butter in the same pan set over a medium heat. Add the shallots and chilli flakes and season with some salt and pepper. Cook, stirring regularly, for 5–6 minutes, until the shallots are nice and soft. Use a spatula to move the shallots to the side of the pan, then crack in the eggs. Season with salt and pepper and sprinkle over the thyme leaves. Cook the eggs until they’re just set, then gently flip them, if you prefer them, like I do, over-easy.
Place 1 rosti on each of 4 warmed plates. Top each with a fried egg and scatter over the spiced shallots. Serve at once.