Preheat the oven to 350°F. Line two baking sheets with parchment paper.
In a large bowl, stir together brown sugar, melted butter, applesauce, and vanilla. In another bowl, whisk together oats, flour, baking soda, cinnamon, and salt. Fold flour mixture into the sugar mixture just until combined. Fold in apple chunks.
Divide the dough into 1 ½ tablespoon-sized balls using a spring-loaded scoop, about 1 inch apart, and flatten slightly. Bake for 10-12 minutes or until golden brown and dry around the edges but still soft in the center.
Cool on the baking sheet for 5 minutes, then transfer to wire racks to cool completely.
Tip: These apple oatmeal cookies are best eaten the day they are made. Only make as many or as little as you intend to eat or share.