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 and set on clean surface. 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, cover and let rise until doubled, about 60-90 minutes.
Punch down dough and turn out onto a clean surface. Cut dough into 16-20 equal pieces. Using the heel of your hand, quickly and firmly roll each piece around in circles until it forms a tight little ball. Arrange rolls in a greased 9 x 13-inch pan. Cover with greased plastic wrap. Let rise for about 1-1 1/2 hours. They will have doubled in size and be puffy.
Meanwhile, preheat oven to 350°F. After the rolls have risen, uncover and place in oven and bake for 20-25 minutes, until golden brown.