Make the dough: Whisk the flour, sugar, salt, and yeast together in a large bowl. Set aside.

Combine the milk, water, and butter together in a heatproof bowl. Microwave or use the stove and heat until the butter is melted and the mixture is warm to touch (about 110°F). Pour into the dry ingredients, add the egg, and stir until it forms a soft dough or use your mixer.

On a lightly floured surface using floured hands, knead the dough for 3 minutes. Place in a lightly greased bowl (I use non-stick spray), cover loosely, and let rest for about 10 minutes.

Fill the rolls: After 10 minutes, roll the dough out in a 14×8 inch rectangle. Spread the softened butter on top. Mix together the cinnamon and sugar. Sprinkle it all over the dough. Roll up the dough tightly to make a 14 inch log. Cut into 10-12 even rolls and arrange in a lightly greased 9-inch round cake pan or pie dish.

Rise: Tightly cover the rolls with aluminum foil or plastic wrap and allow to rise in a warm, draft-free environment for 60-90 minutes. See blog post above for my trick to this step

Bake the rolls: After the rolls have doubled in size, preheat the oven to 375°F (190°C). 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.

Make the icing: Whisk the confectioners sugar, vanilla extract, and coffee/milk together. Drizzle or spread over warm rolls.

Cover leftover frosted or unfrosted rolls tightly and store for up to 3 days at room temperature or up to 5 days in the refrigerator.