Cook the cubed pumpkin over low heat until tender. Then, drain and mash until lump-free. Cool slightly.
Add the water, sugar, and yeast to a small bowl and briefly stir. Let the mixture sit for 5 minutes or until foamy.
In a large bowl, add the pumpkin puree, yeast mixture, flour, butter, and salt. Mix and knead for 5 to 10 minutes until you form a smooth dough. It will be slightly sticky. If it's too tacky to knead, add a small amount of flour. It should be soft and elastic towards the end of kneading time.
Place the dough in a lightly greased bowl, and let it rise at warm room temperature for 1 hour or until doubled in size.
Punch down the dough, then divide it into small balls.
Arrange them on a greased baking pan, close together.
Cover with a towel and let the rolls rise in a warm room temperature for about 30 minutes or until they start to touch each other.
Preheat the oven to 350°F towards the end of the rising time.
Whisk together the yolk and milk.
Brush the rolls with the egg wash, then bake for 30 minutes or until golden brown.