Place the cubed beetroot and parsnip in a large roasting tin. Drizzle with olive oil and sprinkle with thyme, salt and pepper. Toss to coat. Spread evenly in one layer across the roasting tin being careful not to overcrowd the tin otherwise the vegetables will steam instead of roast.
Roast the vegetables in the preheated oven until tender and slightly caramelised, about 15 to 20 minutes.
Remove from oven and let cool to warm, then toss with the crumbled feta. Serve immediately.