Melt butter in a saucepan over medium heat. Add apples, brown sugar, cinnamon, ginger, and salt. Stir to coat the apples, then reduce heat slightly and sauté apples until softened. Meanwhile, make the oats.
Combine milk and water in a large pot and bring to a boil. Stir in oats, brown sugar, cinnamon, and salt, and reduce heat to medium.
Cook oats, stirring occasionally, until softened and mixture is thickened to your liking. This will take 5-10 minutes, depending on how thick you like your oatmeal. (If you accidentally make the oats too thick, stir in more milk or water to loosen.)
Serve oats with a scoop of the cooked apples and a sprinkling of the chopped pecans.