Heat the milk in a large saucepan over medium-low heat until a thermometer registers 185 degrees F. (The milk should be steaming but not boiling.) Turn off the heat and slowly whisk in the dry milk. Whisk in the maple syrup, if using. Let the milk mixture cool to 110 degrees F, 20 to 30 minutes. Whisk in the plain yogurt.
Pour the milk mixture into a large jar or glass bowl. Cover with a kitchen towel or plastic wrap vented with a few holes. Set aside in a warm place (90 degrees F to 105 degrees F), such as near a heater or in a cooler with a thermos filled with hot water, 12 to 18 hours. (The longer it sits, the thicker and tangier the yogurt will be.)
Transfer the yogurt to the refrigerator; chill at least 8 hours. Stir before serving.
For the Apple Compote:
Combine 6 cups diced peeled Granny Smith apples, 1/4 cup brown sugar, 1 teaspoon vanilla extract, 1/4 teaspoon ground cinnamon, a pinch of salt and 1/4 cup water in a skillet over medium heat. Simmer until soft, stirring, about 30 minutes.