Preheat the oven to 350°F (175°C). Line an 8x8-inch baking pan with parchment paper or lightly grease it with butter.
Combine the dry ingredients: In a large mixing bowl, stir together rolled oats, flour, baking powder, cinnamon, nutmeg, and salt.
Mix the wet ingredients: Add melted butter, brown sugar, egg, and vanilla extract. Stir until well combined.
Fold in the apples: Gently add the diced apples (and any optional add-ins) until evenly distributed throughout the batter.
Spread and bake: Pour the mixture into the prepared pan and smooth the top. Bake for 25–30 minutes, or until golden brown and firm around the edges.
Cool and slice: Allow to cool in the pan before cutting into bars. Serve warm or at room temperature.