Heat 1 1/2 teaspoons oil in a large nonstick skillet over medium-high heat; cook apple slices, stirring until golden (about 2–3 minutes). Transfer to a plate. Add remaining 1 1/2 teaspoons oil to skillet; cook chopped apple and shallot over medium heat, stirring until golden (about 2–3 minutes).
Place soup in a large saucepan; bring to a boil. Stir in chopped apples and shallot, nutmeg, and cinnamon; simmer until apples are tender (about 6 minutes).
Ladle the soup into bowls; top with the remaining cooked apple slices. Dust with freshly grated nutmeg, if desired; serve.