Homemade Caramelized Applesauce

Makes 2 to 2-1/2 cups
Peel and core the apples. Cut them into 2-inch chunks. Place the apples in a heavy-bottomed saucepan. Add the remaining ingredients. The sugar will dissolve when heated.
Over medium-high heat, bring to a boil. The apples will fall apart and the ingredients will start to melt into a thick apple soup. Cook down over high heat, about 30 to 40 minutes. Do not stir until the water has evaporated and the sugar turns into a brown film, caramelizing on the bottom of the pan. This caramelization is your indication to lower the flame to medium-low. Now stir and turn over the apples a few times to create a new crust.
Each time the bottom of the pan becomes caramelized, stir the sauce. Continue to use a spoon (wooden is best) to break up the apples.
The applesauce is done when the apples are cooked through and little chunks remain. The sauce will be a deep caramel color. This will take about another 25 to 30 minutes.
Remove the cinnamon sticks before serving, or keep them in for a rustic look.