Preheat the oven to 350 degrees F and line a muffin pan with paper liners. In a large mixing bowl, cream together the sugar, eggs, coconut oil, applesauce and vanilla. Sift together the flour, baking soda, salt, cinnamon and nutmeg. Add these dry ingredients to the wet ingredients and mix well until combined. Stir in the walnuts, if using. The batter will be very thick. Gently add the diced apples and toss.

Using an ice cream scoop or large spoon, fill each of the muffins cups with the batter until almost completely filled. Sprinkle the top of each muffin with brown sugar. Bake the muffins for 20-25 minutes until lightly golden brown or until a wooden skewer comes out with scant dry crumbs. Let the muffins cool before removing them from the tray. Store in an airtight container for up to 3 days.