Peel potatoes and cut them into quarters or sixths. Place them in a pot.
Sprinkle 1 t. salt over potatoes and then cover with 1 inch of water.
Bring potatoes and salt to a boil, cooking until potatoes break apart when poked with a fork (about 20 minutes).
Chop stick of butter into smaller pieces, and place butter and yogurt into the bottom of a stand mixer bowl.
Drain potatoes and put them in the bowl on top of butter and yogurt.
Using the whisk attachment, mix potatoes on on low at first, and slowly increase to power 4-5, until well combined.
Stir in milk gradually on low speed until well combined. Then speed up the mixer to beat the potatoes until smooth.
Add 1 t. salt and pepper to taste.