My Great Grandma was full German so I've had perogies several times growing up and they were similar to a potsticker.
I went out to dinner the other night to a Polish place and we ordered perogies for an appetizer and they were shaped like the ones of my youth but they were like little deep fried pies filled with mozzarella. Yummy, little fried pies but fried pies just the same. So, my question..when you have perogies what are yours like??