Into a medium saucepan, add the apples, brown sugar, lime juice and water. Cover the pot tightly and heat to boiling. Reduce heat to a simmer and cook for 5-8 minutes, until apples are tender. Transfer to a blender or food processor and pulse 3-4 times to desired consistency. If you like it chunky, process it less -- or for uber-smooth -- pulse a few more times. Serve chilled or at room temperature.