Put potatoes in a sauce pan with cold water. Bring to a boil and cook approximately 25 minutes. Potatoes are done when they are tender when pierced with a fork. Drain potatoes and mash immediately.
While potatoes are cooking, sauté vegetables in 1 tablespoon butter.
Preheat oven to 375 degrees.
Beat remaining tablespoon butter along with the milk into the mashed potatoes.
Add the vegetables, flour, eggs, baking powder, salt and pepper and mix well.
Spray muffin pan with cooking spray or fill wells with cupcake liners. See Note 1. Divide potato mixture evenly between the 12 wells. They will be fuller than they would be for a muffin batter. The potato puffs will rise and then deflate so you can fill wells to the brim.
Bake 35-40 minutes. Let stand for about 5 minutes before removing from the pan.
The potato muffins freeze well after baking. Just thaw and reheat gently in the microwave or oven.