Chop the apple into thin, even slices, leaving the peel on for added crunch and tartness.
In a small skillet, melt the butter over medium heat and add the cinnamon, stirring until fragrant—this should take about 30 seconds and will release a warm, spicy aroma.
Add the sliced apple to the skillet and sauté for 2-3 minutes until the edges start to soften and the aroma intensifies, but the slices still retain some crunch.
Meanwhile, combine the oats and water (or milk) in a saucepan and bring to a gentle boil over medium heat.
Reduce the heat to low and simmer, stirring occasionally, for about 5-7 minutes until the oats are tender and the mixture thickens to a creamy consistency.
Once the oats are cooked, gently fold in the sautéed apple slices along with any juices from the pan to incorporate their flavors into the oatmeal.
Allow the mixture to heat through for another minute, letting the apple slices soften slightly and the cinnamon aroma infuse the oats.
Serve hot, garnished with a dusting of additional cinnamon if desired, and enjoy the contrasting textures of creamy oats, tender apple slices, and crunchy peel.