Preheat the oven to 350 degrees F.
Fill a muffin tin with liners.
In a medium bowl, whisk together the flour, cinnamon, allspice and baking soda. Set aside.
In a large mixing bowl, beat together the butter and sugar until creamy and fluffy.
Beat in the eggs, applesauce and vanilla until smooth.
In a small bowl, add the raisins and about 2 tbsp of the flour mixture and toss to coat.
Gradually add the dry ingredients to the wet ingredients, folding just until moistened.
Fold in raisins.
Divide the batter into the prepared muffin tin using a cookie dough scoop.
Bake for 20-25 minutes or until a toothpick inserted in the center comes out clean.
Cool on a wire rack.
Serve at room temperature or warm.
Store any leftovers in an airtight container.