1. Warm the milk in the microwave to 100 degrees F. Add the sugar and the yeast. Let sit for 5-7 minutes to allow the yeast to activate.
2. Whisk together the salt, nutmeg, and flour in a small bowl.
3. Pour the yeast mixture into the bowl of a stand mixer. Add the melted butter, pumpkin puree, egg, kosher salt, nutmeg, and flour.
4. Using the paddle attachment, mix at low speed until the ingredients are well combined and the dough has come together.
5. Change the attachment to the dough hook and kneed on medium-low for 15 minutes. If the dough is very wet, you can add a little more flour; if the dough is dry, add a little more milk. The dough should be very sticky.
6. Place the dough in a large well-greased bowl and cover with a tea towel and leave in a warm spot. Allow the dough to rise until doubled 1 ½ to 2 hours.
7. Scoop the dough out on to parchment paper that has been sprayed with cooking spray.
8. Divide the dough into 16-20 pieces depending upon the size of the rolls you
like.
9. With greased hands, shape the pieces into balls by first pinching the edges into the center, then rolling the ball on the parchment paper to create surface tension.
10. Place the rolls into a well-greased 9 x 13-inch baking dish.
11. Cover with a towel and allow to rise again for 1 ½ - 2 hours.
12. Preheat oven to 375 degrees F.
13. To prepare the egg wash, whisk the egg and water together in a small bowl and brush the tops of all the rolls using a pastry brush.
14. Once the buns have risen, bake for 25 – 30 minutes or until golden brown. You can use an instant-read thermometer to check the internal temperature. It should read 200F when inserted into the middle of a bun. Allow cooling in the pan for 10 – 15 minutes.
15. Remove the buns and place onto a cooling rack to cool further.
16. Serve the rolls warm or at room temperature with butter and honey.