Whisk together oil and sugar. Add eggs, vanilla, and buttermilk and whisk or beat till well combined. Stir in the diced apple.
In a small bowl, whisk together the flour, baking powder, salt, and cinnamon. Stir into wet ingredients.
Divide batter evenly between 48 mini muffin cups that have been well greased. Bake at 350° for about 16 minutes or till lightly browned around the edges. Remove to cooling racks.
Combine the sugar and cinnamon in a small bowl. Brush the tops of the muffins with butter, then roll muffins in cinnamon sugar mixture. Serve warm.