Preheat oven to 375 degrees F. Brush butter into regular sized muffins cups, coating the bottom and sides of each cup. Set aside.
In a medium sized bowl, whisk together milk, eggs, cinnamon and vanilla.
Unwrap package of cinnamon rolls and set icing aside. Cut rolls into 8 pieces each and place in the egg mixture, stirring to coat.
Divide mixture into muffin cups. Spoon any remaining egg mixture over the top of each cup.
Drizzle each cup with about half a teaspoon of maple syrup.
Bake for about 15 minutes, or until tops are golden brown.
Pour icing into a microwaveable container and heat for 7-10 seconds, just until icing is pourable. Spoon over each muffin.
Using a knife to loosen, gently remove muffins from the pan and serve warm.