In a medium mixing bowl whisk together the milk, pumpkin puree, butter and egg until smooth.

In the bowl of a stand mixer fitted with a dough hook (or with a large mixing bowl and a mixing spoon if working by hand) add in flour, sugar, yeast, and salt and give a stir to mix everything together.

On medium speed, pour in the wet ingredients into the dry and mix for roughly 8 minutes until it forms a dough and pulls away from the sides of the bowl. If you dough is a tad dry add a splash more milk until the dough forms. (If kneading by hand, knead the dough for 10 minutes.)

Transfer the dough to a large, oiled bowl and cover tightly with plastic wrap and a kitchen towel. Set aside at room temperature to proof for 60 - 90 minutes, or until doubled in size.

Punch the dough down and transfer it to a floured work surface. Divide the dough into 16 equal pieces, then shape it into rolls and arrange them in a 10-inch (25-cm) round baking pan with 10 rolls on the edge, then 5 rolls, then one roll in the center.

Cover again and let rise in a warm place until doubled in size, 45-60 minutes.

At the end of the rising time, preheat the oven to 350°F (180°C).

Brush the rolls with the egg wash, then bake for 30-35 minutes, until golden brown. Brush with butter while the rolls are still hot.

Let cool in the pan for 10 minutes before serving. Serve warm or at room temperature.

Store leftovers in an airtight container for up to 3 days. For longer storage, freeze for up to 2 months. Defrost at room temperature for about an hour, and rewarm in a 250°F (120°C) oven for 5 minutes.