Preheat the oven to 400 degrees F.  Combine 4 tablespoons of the butter with 1 cup of the sugar and a tablespoon of water in a 10- or 12-inch nonstick ovenproof skillet and turn the heat to medium.  Cook, shaking the pan occasionally, until the sugar melts into the butter and the mixture bubbles. Turn off the heat and add the apples in layers; about halfway through, dot with some of the remaining butter and sugar.  Use the rest of the butter and sugar on top of the last layer, along with the cinnamon.  Put in the oven.
Bake, undisturbed, until the apples give up their liquid and it evaporates and the sides of the mass are dark brown and sticky looking.  This will take about 45 minutes, more or less, depending on your apples' water content.  Remove and let cool.