In a medium bowl, stir together apple, brown sugar, salt, cinnamon, and nutmeg until combined. Stir in lemon juice and vanilla.
In a medium saucepan, melt butter over medium-high heat. Cook until lightly browned, about 3 minutes. Reduce heat to medium; add apple mixture and 2 tablespoons (30 grams) water, stirring until combined. Bring to a boil.
In a small bowl, whisk together cornstarch and remaining 2 tablespoons (30 grams) water. Slowly add cornstarch mixture to apple mixture, stirring constantly. Return mixture to a boil, and cook, stirring frequently, until thickened and translucent and apples are tender, about 4 minutes. Keep warm until ready to use.