Make the cookies
Preheat oven to 350.
Combine butter and sugar in bowl of stand mixer.
Beat for 2 minutes on low speed using paddle attachment.
Add eggs, one at a time, and mix until combined.
Add yogurt and vanilla, mixing until incorporated.
Add baking powder, soda, salt, and flour. Mix on low.
Form dough into a ball the size of a walnut. Place on cookie sheet, leaving 2 inches between cookies.
Flatten balls of dough slightly.
Bake for 12 minutes. (They will not be golden.)
Cool completely.
Make the frosting
Combine butter, 2 cups sugar, and vanilla. Mix well. Add milk, as needed.
More sugar can be added if you prefer a sweeter frosting.
Frost cookies, as desired.