Simmer apples, butter, cinnamon, brown sugar, and vanilla on the stovetop over medium-low heat for 10 minutes or until the apples are soft and the sauce has thickened.
Open the can of cinnamon rolls and set aside the icing for later. Cut each cinnamon roll into small pieces.
In a mini bundt pan, divide half of the cinnamon roll dough between the six wells, and top with a generous spoonful of apples and brown sugar sauce.
Place the remaining half of the cinnamon roll dough pieces on top of the apples and top with another spoonful of brown sugar sauce.
Bake for 16-20 minutes or until the tops are golden brown.
Allow the monkey bread to cool in the pan for 10 minutes, and then run a knife around the edges to loosen them from the pan. Carefully remove the monkey bread from the pan and place them on a serving platter or individual plates.
Drizzle the icing over each of the monkey breads and serve warm.