Whisk flour, sugar, salt, and yeast together in a large bowl. Set aside.
Combine milk, water, and butter together in a bowl. Microwave or use the stove and heat until the butter is melted and the mixture is warm.
Pour into the dry ingredients.
Add egg and stir until it forms a soft dough.
On a lightly floured surface, gently knead the dough.
Place in a lightly greased bowl, cover loosely and let rest for about 10 minutes.
Filling
Roll the dough out in a 14×8 inch rectangle.
Spread the softened butter across.
Mix together the cinnamon and sugar. Sprinkle it all over the dough.
Roll up the dough tightly.
Cut into even rolls.
Arrange in a lightly greased 9-inch round dish.
Tightly cover the rolls with plastic wrap and allow to rise for about 1-1.5 hours.
Bake
After the rolls are about doubled in size, preheat the oven to 375°F.
Bake for 25-28 minutes until lightly browned. If you notice the tops are getting too brown too quickly, loosely cover the rolls with aluminum foil and continue baking.
Icing
Whisk powdered sugar, vanilla extract, and milk together.
Spread over warm rolls.
Serve and enjoy.
Notes
Try using strong brewed coffee in the icing for a different flavor.