In a small bowl, sprinkle the yeast over the warm milk. Stir to combine and let sit until frothy, about 10 minutes.
In the bowl of a stand mixer fitted with a dough hook or a large bowl, combine the flour, sugar, and salt. Slowly mix in the frothy yeast with the milk, followed by the pumpkin puree, softened butter, and egg to form a soft, smooth, and slightly sticky dough.
On a lightly floured surface, knead the dough until smooth and elastic, then transfer to a large bowl, cover with plastic wrap or a towel, and allow to rest at room temperature until doubled, 1-2 hours.
Grease a 9 x 13 inch (23 x 33 centimeter) baking dish with butter.
On a lightly floured surface, divide the dough into 12 equal pieces.
Form each piece into a smooth ball, seam side down, and arrange in the greased baking dish about 1 inch (2.5 centimeters) apart.
Cover the baking dish with a towel and allow to rise at room temperature until puffed, about 30 minutes.
Preheat oven to 375˚F (190˚C) and place the oven rack in the center.
In a small bowl, beat together the egg yolk and milk.
Gently brush the egg wash over the risen rolls.
Transfer the baking dish to the preheated oven and bake until the rolls are golden, 12-15 minutes.
Remove the baking dish from the oven and brush with the melted butter.
These Pumpkin Yeast Rolls are best served warm.