Prepare the apples. Peel and core the apples, then finely dice them into small pieces so they cook quickly and evenly.
Cook the apple mixture. Add the diced apples, butter, brown sugar, cinnamon, nutmeg, and salt to a small saucepan. Cook over medium-low heat, stirring occasionally, until the apples become tender and fragrant.
Add the oats. Stir the old-fashioned oats into the cooked apples. Continue cooking briefly until the oats absorb some of the warm apple and cinnamon flavor.
Warm the oat milk. Heat the oat milk gently in a saucepan until steaming but not boiling. Stir in the vanilla extract and maple syrup.
Froth the milk. Use a milk frother to create a light, creamy foam. If you don't have a frother, whisk the warm oat milk vigorously.
Add the coffee. Divide the strong brewed coffee between four mugs.
Add the apple mixture. Spoon some of the warm apple-oat mixture into each mug and gently stir it into the coffee.
Pour in the oat milk. Slowly add the warm, frothy oat milk to each mug, leaving some foam on top.
Garnish and serve. Top with whipped cream if desired, then sprinkle with cinnamon and add a small spoonful of the apple mixture. Serve warm.