Preheat the oven to 350°F (175°C). Lightly grease a 12-cup muffin tin or line it with silicone muffin liners.
In a large bowl, combine the rolled oats, baking powder, ground cinnamon, and salt. Stir to mix evenly.
In a separate medium bowl, whisk together the mashed banana, eggs, milk, maple syrup, vanilla extract, and applesauce until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Fold in the chopped walnuts gently to distribute them evenly.
Spoon the mixture evenly into the prepared muffin tin, filling each cup about 3/4 full.
Bake for 22 to 25 minutes, or until the oatmeal cups are set and a toothpick inserted into the center comes out clean.
Allow the oatmeal cups to cool in the pan for 10 minutes, then transfer them to a wire rack to cool completely.
Once cooled, place the oatmeal cups in a single layer on a baking sheet and freeze for 1 hour.
Transfer the frozen oatmeal cups to a resealable freezer-safe bag or airtight container and store in the freezer for up to 3 months.
To reheat, microwave a frozen oatmeal cup for 30 to 45 seconds or until warmed through.