Peel the apple if desired, remove the core, and cut it into small, even pieces.
Add the diced apple, optional butter, and a splash of milk to a medium saucepan. Cook over medium heat for about 3–4 minutes, stirring occasionally, until the apple begins to soften.
Stir in the rolled oats, remaining milk, cinnamon, and salt.
Bring the mixture to a gentle simmer, then reduce the heat to low.
Cook for about 5–7 minutes, stirring regularly, until the oats are tender and creamy and the apples are softened.
Remove the saucepan from the heat and stir in the maple syrup or honey and vanilla extract.
If the oatmeal is too thick, add a small splash of milk and stir until it reaches your preferred consistency.
Divide the oatmeal between two bowls.
Top with chopped walnuts or pecans, Greek yogurt, raisins, fresh apple slices, extra cinnamon, or maple syrup as desired.
Serve warm.