On a plate combine sugar and cinnamon. Heat a very large skillet over medium heat; add butter. Press the cut side of each apple into the cinnamon-sugar mixture. Place apples, cut sides down, in the hot skillet. Sprinkle with any remaining cinnamon-sugar mixture.
Cook apples for 7 to 8 minutes or just until apples begin to brown. Add the 1/2 cup water. Cover; reduce heat to low. Simmer for 5 to 7 minutes, adding more water if sugar begins to burn.
Remove apples from skillet; place 2 apple halves on each of 4 plates; drizzle with sauce from skillet. Add a scoop of ice cream to each plate. If desired, sprinkle with cinnamon sugar.