Cut cauliflower head into quarters.
Pour water or broth into Instant Pot. Place trivet in pot. Place potatoes, cauliflower and garlic on top of trivet. Seal pot and cook at high pressure for 4 minutes. Let pressure naturally release 10-15 minutes, then release remaining pressure.
Place cauliflower in food processor and process until smooth, scraping down the sides with a spatula.
Remove trivet from Instant Pot, leaving broth, garlic and potatoes in pot. Mash until smooth (leave a few chunks if you like some texture). Add pureed cauliflower, butter and yogurt to pot. Mix until blended. Season to taste with salt and pepper. Garnish with chives.
Cut cauliflower into florets. Cut potatoes into 1" slices.
Add enough water to a large pot to just cover the potatoes. Bring to a boil. Add potatoes. Place steamer basket over potatoes; place cauliflower and garlic on top. Cover and steam cauliflower for 10 minutes (it should be tender); remove. Cover pot and continue to cook potatoes until tender, about another 10 minutes.
Meanwhile, place cauliflower ad garlic in food processor and process until smooth, scraping down the sides with a spatula.
When potatoes are tender, drain and mash potatoes until smooth. Add pureed cauliflower, stock, butter and yogurt. Beat until blended. Season with salt and pepper. Garnish with chives.