Preheat the oven to 375°F. Line muffin tins with paper liners or grease with nonstick spray.
In a large bowl, mix the dry ingredients: the flour, baking powder, baking soda, salt, nutmeg, and cinnamon. Whisk until there are no lumps
In another bowl, beat together the applesauce, sugar, eggs, oil, yogurt, and vanilla extract until smooth.
Add the wet ingredients to the dry ingredients and stir until just combined. Do not overmix.
Spoon the batter into the prepared muffin tin, filling each cup about 3/4 full.
Bake for 15-20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Allow the muffins to cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.