Preheat your oven to 425°F and line a 12-cup muffin pan with paper liners. The high starting temperature helps the muffins rise quickly for that nice bakery-style dome, so make sure your oven is fully preheated before the batter goes in.
In a skillet heated to medium high heat add 1/2 stick butter, 1/4 cup sugar, 1/2 tsp cinnamon and diced apples. Cook together until apples are soft and butter has caramelized. Set aside to cool.
In a medium bowl, whisk together the flour, baking powder, cinnamon, nutmeg, and baking soda. Set that aside.
In a large bowl, whisk the melted butter, sourdough starter, egg, sour cream, sugar, and vanilla extract until the mixture looks smooth and creamy. It’s okay if the sourdough starter leaves a few small streaks; that’s normal.
Add the dry ingredients to the wet mixture and stir gently until combined. The batter should be thick, not runny. If it feels too loose, add a tablespoon or two of flour. Gently fold in the apples, being careful not to overmix so they don’t burst and turn the batter purple.
Spoon the batter evenly into the prepared muffin cups, filling each nearly to the top. Sprinkle a little turbinado sugar on each muffin for a crunchy, golden finish.
Bake the muffins at 425°F for 15-18 minutes, or until a toothpick inserted into the center comes out clean.
Let them cool in the pan for about five minutes, then move them to a wire rack to finish cooling completely.
Once cool, the muffins can be stored in an airtight container at room temperature for up to three days. You can also freeze them individually and warm them up later in the oven or microwave when you need a quick breakfast or snack.