Add milk and butter to a sauce pan and bring to a boil. Remove from heat and stir in mashed potatoes and honey. Set aside.
Add yeast to warm water and stir together. Set aside.
Add potato mixture into mixer bowl with the dough hook. Add 2 cups of flour and mix until combined. Add eggs, mixing until incorporated. Add yeast mixture and mix together.
Add 2 more cups of flour and salt and continue to mix until dough comes together. Add enough of the remaining flour, ½ cup at a time, until dough starts to pull away from the sides of the bowl.
Pour into a greased bowl, cover and allow to rise 1 hour.
Punch down dough. Turn dough out onto a flat surface, kneading out any air bubbles.
Divide dough in half, using additional flour if dough is too wet/sticky. Divide each half into 16 pieces. Using the palm of your hand, roll each piece on coutertop to form a smooth, round roll.
Place in greased baking pans about 1 inch apart. Sprinkle with shredded cheese, pressing lightly to hold it in place. Cover and let rise until indentation remains after lightly touching roll with finger.
While rolls are rising, preheat oven to 375°F
Bake rolls for 20-25 minutes or until golden brown.
Remove from the oven to a wire rack. Serve immediately or at room temperature.