Preheat oven to 375°F and fill a 12-cup muffin tin with paper liners.
In a large mixing bowl, whisk together butter, brown sugar, ½ cup granulated sugar, vanilla, buttermilk, pumpkin, and two eggs. Whisk until well combined.
In a separate bowl, combine flour, salt, cinnamon, cloves, nutmeg, baking powder, and baking soda.
Add the dry ingredients to the pumpkin mixture and stir just until combined - some lumps in the batter are okay.
In a third bowl, use a hand beater to combine cream cheese filling ingredients. Beat until smooth.
Transfer the muffin batter to the muffin tin, filling each cup about ¾ full.
Make a dip in the center top of each muffin to create a little “bowl” for the cream cheese filling.
Use a piping bag or a spoon to fill the indentations in the muffins with the cream cheese filling. If you are using a piping bag, you can squeeze some of the filling down inside the muffin batter, too!
Bake for 20-25 minutes, until the cream cheese filling is set (no longer wet) and a toothpick inserted in the muffin (cake part only) comes out with just a few crumbs.
Cool the muffins for just a few minutes in the pan before transferring to a cooling rack to cool the rest of the way.