In a small saucepan, heat the milk over low heat until it's warm but not boiling. Remove from heat and stir in the softened butter and sugar until the butter melts and the sugar dissolves. Let it cool for a few minutes. Add pumpkin puree and salt and stir until well combined.
In a separate small bowl, dissolve the yeast in warm water and let it sit for about 5 minutes until it becomes foamy.
Add the activated yeast mixture and the egg to the pumpkin mixture and mix well.
Gradually add the flour, one cup at a time, mixing well after each addition. Continue adding flour until the dough becomes soft and slightly sticky.
Attach the dough hook attachment to your electric mixer.Increase the speed to medium and let the electric mixer knead the dough for about 5-7 minutes until it becomes smooth and elastic.
Place the dough in a greased bowl, cover it with a clean kitchen towel, and let it rise in a warm place for about 1-2 hours, or until it doubles in size.
Punch down the risen dough, divide it into two portions, and roll each portion into a log. Cut small portions of dough and shape each portion into a ball.
To shape the balls into pumpkins, use a piece of thread or thin string. Gently press the thread into the center of each roll, about halfway through, and then pull the ends of the thread up and over the top to create pumpkin-like divisions.
Cover the shaped rolls with a clean kitchen towel and let them rise again for about 30-45 minutes, or until they puff up slightly.
Preheat your oven to 375°F (190°C).
Brush the rolls with melted butter and bake them in the preheated oven for about 15 minutes, or until they turn golden brown.
Serve the pumpkin dinner rolls warm or at room temperature and enjoy.