Bring a medium pot to medium-high heat on the stovetop. Add just a bit of water to prevent sticking, and then your apple and peach to the pot.
Cook your apple and peach for 10-15 minutes, or until your peaches have started to break apart and your apple can be very easily pierced with a fork (this time may vary a bit depending on the size of your apple and peach pieces). Add water as needed to prevent sticking. (Note that if you are doubling this recipe, this step will take longer since the apples and peaches are more crowded).
Turn off the heat and add your cooked apples and peaches to a high speed blender. If using, add the optional maple syrup and cinnamon to the blender as well.
Blend until mostly smooth (applesauce tends to have just a tad bit of texture, so we don't want it 100% smooth). If your mixture is too thick, you may add splashes of water to the blender as needed.
Allow your applesauce to come to room temperature, and then refrigerate. Best enjoyed cold, but can also be enjoyed warm if you prefer!
Enjoy!