Dice up the potatoes and cauliflower into bite-size pieces.
Put potatoes, cauliflower, and garlic all into a large pot, add in enough water to just cover the potatoes and cauliflower, and simmer until soft (about 30 minutes).
Once cooked, drain the water, and put the cauliflower, potatoes, and garlic back into the pot.
Take a sharp knife and chop through your potatoes and cauliflower while they’re still in the pot, just to make the chunks a bit smaller.
Add olive oil, yogurt, and 2/3s of the milk and blend. Then take a hand-held blender or immersion blender and blend the mixture until smooth and the texture is similar to traditional mashed potatoes. If needed, add the remaining milk and blend to thin.