Place the beetroot and potatoes in a large pot, cover with cold water and season with salt. Bring the water to a boil, then turn the heat down and simmer for 20 to 25 minutes, until both the potatoes and beets are tender.
Drain the vegetables and place into a food processor, blitz until mashed together and well combined.
Alternatively, mash the vegetables in the pot using a potato masher.
Stir in yogurt, butter, and season with salt and pepper. Serve immediately.
