Pour the warm milk into a small bowl and sprinkle the yeast over the top. Let sit for a minute before stirring to dissolve. Let sit about 10 minutes, until frothy.
In the bowl of a food processor fitted with a dough blade, beat together the melted butter and sugar. Mix in the egg and then the pumpkin puree. Add the frothy yeast and milk.
Slowly add the flour, a little at a time, and the salt until a soft dough comes together. It should be slightly sticky. Use lightly floured hands to knead the dough until smooth and elastic. Add a little flour if needed, just enough to make the dough workable. Don't add too much or the rolls will become tough. Place the dough an oiled bowl, cover, and allow to rise until doubled, about 1 1/2 hours.
Punch down the dough and divide into 12 pieces on a lightly floured surface. Form each piece into a ball and place in a greased 9x13 inch baking dish about 1 inch apart. Cover the pan with a towel and rise until puffed, 30 minutes to 1 hour. Preheat oven to 350˚F.
Brush the tops of the rolls with additional melted butter and bake in the preheated oven until the tops are golden, 20-23 minutes. Serve warm with butter or pumpkin butter.