Preheat the oven to 350°F, and adjust a rack to the center. Line a muffin tin with 12 paper cups. Set aside.
In a large mixing bowl, combine the mashed sweet potato (see notes on how to mash the potato), buttermilk, eggs, oil, sugar and salt. Mix until smooth -- you can use an electric mixer if that's easier.
Add the flour and baking soda and mix only until it's incorporated.
Fold in ⅔ cup of the grated cheese and the rosemary.
Fill each paper muffin cup about ¾ the way up with the batter.
In a small bowl, mix the softened butter with the remaining ⅓ cup of grated cheese and then evenly distribute this on top of each batter-filled cup.
Bake in the preheated 350°F oven until the muffins are set and becoming golden, 20 to 25 minutes.
Let them cool for at least 10 minutes before serving.