Rolls: In a small saucepan, heat milk and 2 tablespoons butter until warm and butter is almost melted, stirring constantly. In a large mixing bowl, combine pumpkin, sugar, nutmeg, all-spice and salt.
Add the milk mixture to the pumpkin mixture and beat with an elastic mixture until fully combined. Beat in egg and yeast.
Add 1 cup flour to the pumpkin mixture and beat at a low speed for 5 minutes. Add the remaining flour mixture and mix until fully combined.
Grease a large bowl and place dough in it, turning to coat. Cover and let rise in a warm place until doubled (around 1 hour).
Punch dough down. Turn onto a floured surface and knead a couple of times until dough is smooth. Roll dough into a 12×10 rectangle.
In a small bowl, combine the sugar and cinnamon. Brush the surface if the dough with the melted butter, then sprinkle with brown sugar mixture.
Beginning with the long side of the dough, roll up jelly style. Pinch seam to seal. With a sharp knife, cut roll into 1 inch slices.
Place rolls cut side up in a greased 11×17 inch baking pan. Cover and let rise until nearly doubled, about 30-45 minutes.
Bake at 350˚F for about 15-20 minutes until golden. Remove from pan to a waxed paper-lined wire rack. Let cool.
Frosting: In a small saucepan, heat butter until melted. Stir in brown sugar and milk. Cook over medium heat for 1 minute. Transfer to a medium bowl, and let cool. Stir in the vanilla, all-spice, salt and confectioners’ sugar. Beat with an electrical mixer until combined. Drizzle over cooled buns.