In saucepan, heat 1/2 cup milk, water, and 2 tablespoons butter until very warm.
Place milk mixture, salt, flour, yeast, sugar, and eggs in the pan of the bread machine in the order suggested by the manufacturer. Select the Dough cycle. Press Start.
Once Dough cycle is complete, remove the dough from the bread machine and punch down. On a floured surface, roll into a large rectangle. Smear with the softened butter.
Combine the cinnamon and 1/3 cup sugar.
Sprinkle over the rectangle. Generously sprinkle the raisins and/or chopped nuts over the top.
Roll the dough up into a log starting at the long side.
Cut into 12 slices.
Place the rolls cut side down into a 9x13-inch greased baking pan. Cover, and let rise in a warm place until almost doubled, about 30 minutes.
Preheat an oven to 375 degrees F (190 degrees C).
Combine the confectioners' sugar, 1.5 tablespoons melted butter, vanilla extract, and 1.5 tablespoons milk into a thick frosting; set aside.
Bake rolls in preheated oven until golden, 20 to 25 minutes.
