Preheat oven to 400 degrees F. Grease twelve 2-1/2-inch muffin cups or line with paper bake cups. For topping, in a small bowl, stir together granulated sugar and the 1/8 teaspoon allspice. Set aside.
In a medium bowl, stir together the flour, brown sugar, baking powder, the 1 teaspoon allspice, the baking soda, and salt. Make a well in the center of the flour mixture; set aside.
In a medium bowl, beat eggs with a wire whisk or rotary beater. Stir in apple butter, melted butter, and vanilla. Add apple butter mixture to flour mixture all at once. Stir just until moistened (batter will not be smooth).
Spoon batter into prepared muffin cups, filling each almost full. Sprinkle with topping. Bake for 18 to 20 minutes or until a toothpick inserted in centers comes out clean.
Cool in muffin cups on a wire rack for 5 minutes. Remove from muffin cups. Serve warm. Makes 12 muffins.