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Add milk, sugar, butter, vanilla and eggs into bread machine. Cover liquids with flour. Top with yeast and salt. Run on dough cycle making sure to check the dough consistency. You want it to be slightly tacky - ball forming, but still be able to touch it with a quick tap and not stick. (See notes for hand mixing instructions.)
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Preheat oven to 375 degrees.
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For the filling, combine the brown sugar and cinnamon in a bowl.
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Place dough onto clean surface and roll into rectangle.
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Spread the softened butter over the surface of the dough, then sprinkle the sugar mixture evenly over the surface.
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Working carefully, from the long edge, roll the dough down to the bottom edge. Cut the dough into 1 1/2 inch slices, and place in a lightly greased baking pan. Let rise in a warm place until doubled in size.
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Bake for 15-20 minutes or until light golden brown.
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While the rolls are baking, combine the icing ingredients, adding the powdered sugar a little bit at a time to avoid a mess.
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Beat well with an electric mixer until fluffy.
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Frost rolls once removed from the oven.