In a mixing bowl combine milk, water, butter, mashed potato flakes, egg, sugar, flour, salt, and yeast. Using a stand mixer fitted with dough hook, knead for 6-8 minutes or until smooth and soft without being too sticky. The dough should clear sides of the bowl but slightly stick to the bottom. Add additional flour one tablespoon at a time if too wet. Add additional milk 1 tablespoon at a time if too dry. Remove from bowl. Using the heel of your hand knead briefly until it forms a nice round ball.
Alternately you can knead by hand on a floured surface until you have a smooth soft dough.
Place dough in a greased bowl and let rise until doubled about 60-90 minutes.
Separate dough into 16-20 equal pieces. Using the heel of your quickly and firmly roll each piece around in circles until it forms a tight little ball. Arrange rolls in a greased 9 x 13 pan. Cover with greased plastic wrap. Let rise for about 1 1/2 hours. They will have doubled in size and be puffy.
Meanwhile, preheat oven to 350°. After the rise, place in oven and bake for 20-25 minutes. Look for rolls that are golden brown.