Preheat the oven to 350°F (180°C). Line a 12-cup muffin tin with paper liners or grease it well with non-stick spray. Set aside.
In a large bowl, whisk together the whole wheat flour, oats, baking soda, salt, and ground nutmeg until well combined.
In a separate medium bowl, stir together the melted butter, maple syrup, mashed bananas, and vanilla extract until smooth.
Pour the wet mixture into the dry ingredients. Stir until just combined — do not overmix. The batter should remain slightly lumpy.
Gently fold in the blueberries (fresh or frozen, unthawed if frozen) using a spatula or wooden spoon.
Divide the batter evenly among the muffin cups. Fill each cup close to the top, as the muffins do not rise significantly.
Bake for about 30 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Let the muffins cool in the tin for 5–10 minutes, then transfer them to a wire rack to cool completely.