Preheat the oven to 425 degrees F.
Place the flour, sugar, baking soda, salt, cinnamon and nutmeg in a large bowl and whisk to combine.
In a smaller bowl, stir together the applesauce, milk, sour cream, eggs, melted butter, and vanilla.
Pour the liquid ingredients into the dry, and fold together until just barely combined (batter will be very thick).
Cover the batter with a tea towel and allow it to rest for 5-10 minutes while you prepare a 12 cup muffin pan with liners.
Divide the batter equally between all 12 wells of the muffin pan, and garnish with turbinado sugar, if desired. I used ¼ teaspoon per muffin, but feel free to use more.
Bake the muffins for 5 minutes at 425 degrees F, then turn the oven temperature down to 350 degrees F and continue to bake for 14 to 18 minutes, or until a toothpick inserted in the thickest part of a muffin comes out clean or with a few moist crumbs.