Preheat oven to 350°F Place muffin papers in muffin tins or spray tins with vegetable oil.
Drain oranges and pat dry with paper towels. Set aside.
Whisk together flour, baking powder, salt, nutmeg, allspice, and sugar. Cut in shortening with a pastry blender or fork until mixture resembles coarse crumbs.
Whisk together egg and milk. Pour into flour mixture and stir with a fork just until combined. Do not overmix. Batter will be thick. (If your batter is crumbly, you may add a SMALL splash of milk). Carefully fold in mandarin oranges.
Fill muffin tins 3/4 full. Bake 20 to 25 minutes until center tests done and muffins are lightly golden.
While muffins are baking, place melted butter in a small bowl. In another small bowl, whisk together sugar and cinnamon.
When muffins are done, dip each hot muffin first into the butter and then into the cinnamon sugar. Let cool.