Step 1: Prepare the pan: Preheat the oven to 350°F. Line an 8-inch square baking pan with parchment paper, leaving enough overhang to lift the cooled bars out of the pan.
Step 2: Mix the wet ingredients: In a large bowl, whisk together the applesauce, peanut butter or almond butter, brown sugar, egg, and vanilla extract until smooth and well combined. Make sure the nut butter is thoroughly incorporated before moving on. This helps distribute the richness evenly throughout the bars.
Step 3: Add the dry ingredients & let it rest: Add the old-fashioned rolled oats, flour, cinnamon, nutmeg, baking powder, and salt. Stir until everything is evenly combined. If you're using walnuts, pecans, raisins, dried apples, or mini chocolate chips, fold them in now. The batter should be thick and moist. It may look wetter than you expect at this point, but that's okay. Let the mixture sit for 10 minutes. This gives the rolled oats time to absorb some of the moisture from the applesauce.
Step 4: Fill the pan: Transfer the mixture to the prepared pan. Use a spatula or the back of a spoon to press the batter into an even layer, making sure it reaches the corners of the pan.
Step 5: Bake & cool completely: Bake for 25 to 30 minutes, until the edges are lightly golden and the center is set but still soft. Start checking toward the lower end of the baking range because oven temperatures and pan materials can vary. The center shouldn't look wet, but it also shouldn't look dry and completely firm. Allow the bars to cool completely in the pan. Once cooled, lift them out using the parchment paper and cut into 8 or 16 bars. The bars become firmer as they cool, so resist the urge to cut them while they're still warm.