Preheat the oven to 350°F (175 °C). Line two 6-cup muffin pans with paper liners. Set aside
In a large bowl, combine the flour, oats, baking, powder, cinnamon, baking soda, and salt.
Whisk the eggs with the sour cream and the brown sugar.
Grate the apples and whisk them into the wet ingredients. Drizzle in the melted butter while whisking to incorporate it.
Pour the wet ingredients into the bowl with the dry ingredients, and stir until just combined.
Fill the prepared muffin cups halfway with the batter, then place 2 berries on top of the batter.
Top with remaining batter and berries (press them down gently to anchor them) and sprinkle the top of each muffin with coarse turbinado sugar or cinnamon sugar and a few extra oats.
Bake for about 45 minutes or until golden. Use a cake tester to make sure the muffins are baked in the middle. It should come out clean and the muffins should spring back when pressed gently.
Let the muffins cool for 5 minutes, then transfer to a wire rack. Serve warm or room temperature.
Notes
You can freeze the muffins. To defrost, place 1 muffin in the microwave and heat for 20–30 seconds (on max power). They should be hot and fluffy and just like they were freshly baked!