Parboil the parsnip in boiling salted water for around 5 minutes. Drain well.
Melt the butter in a small frying pan with the olive oil. Add the radishes and drained parsnips and sauté until golden brown. Add the garlic for the last couple of minutes of cooking.
Make a gap in the middle of the pan and crack the egg in. Cook until the yolk is set to your liking. Sprinkle with parsley and serve.