Warm 1 cup of milk in a small saucepan until it just starts to bubble, then remove from heat. Add ½ cup of butter and stir until melted. Add water and let cool until lukewarm.

Place lukewarm milk mixture, yeast, white sugar, salt, eggs, and 2 cups flour in a large bowl; stir well to combine. Stir in the remaining flour, ½ cup at a time, mixing well after each addition.

When the dough has pulled together, turn it out onto a lightly floured surface and knead until smooth and elastic, about 8 minutes.

Divide dough into two equal pieces. Using a floured rolling pin, roll each piece into a 12x9-inch rectangle.

Stir cinnamon and brown sugar together in a bowl. Spread each piece of rolled dough with ¼ cup butter and half of the cinnamon sugar mixture.

Roll up dough, using a little water to seal the seam.

Cut each roll into 12 slices using a very sharp knife. Arrange rolls cut-side down onto two 9x13-inch greased baking pans. Cover with greased plastic wrap and let rise in a warm place until doubled in volume, about 1 hour.

Preheat the oven to 375 degrees F (190 degrees C).

Bake cinnamon rolls in preheated oven until golden brown, 20 to 25 minutes.

Meanwhile, make the frosting: Beat confectioners sugar, softened cream cheese, 1 tablespoon softened butter, and vanilla together in a bowl. Add milk gradually until frosting reaches a spreading consistency.

Spread frosting over warm (but not hot) cinnamon rolls.

Serve and enjoy.