Put oven rack in middle position and preheat oven to 375. Grease muffin pan.Stir together flour, baking powder, baking soda, spices and salt in a bowl. Whisk together eggs and brown sugar in a large bowl until combined well, then add butter, a little at a time, whisking until mixture is creamy. Stir in applesauce, then fold in flour mixture until flour is just moistened. Stir in nuts and divide batter among muffin cups. Top with coarse sugar. Bake until muffins are puffed and golden, about 20 minutes. Cool pan on a rack for 5 minutes, then remove muffins from pan to cool.
