Preheat oven to 350 and line 24 muffin tins with paper liners.
In an electric mixer with a paddle attachment cream the butter and the 2 sugars for about 5 minutes, scraping down the side mid-way.
Add the eggs one at a time and mix until combined.
Add the applesauce and vanilla and incorporate.
Add all of the dry ingredients.
Finally add the pumpkin puree.
Your batter should be light and fluffy.
Add the muffin batter to each of the muffin tins and bake for about 25 minutes until done.
Let them cool completely.
Make the cream cheese icing -
Combine all the ingredients into an electric mixer for 6-7 minutes. Scrape down the sides every so often. You want to make sure that all the components are thoroughly combined.
Assemble the muffins-
Take one muffin and using a spoon scoop out the center, not completely to the bottom. Place your icing in a zip top bag and cut off a corner. Squeeze the frosting into the muffin and swirl a bit on top.
Everyone knows the icing is the best part- so don't be stingy!