In the bowl of a stand mixer, combine the warm milk, one tablespoon of the sugar, and the yeast. Stir gently and let it sit for about 5 to 10 minutes until the mixture becomes frothy and bubbly.
Add the remaining sugar, pumpkin puree, egg, and melted butter to the yeast mixture. Whisk or use the paddle attachment on low speed until the ingredients are well combined and smooth.
Add the salt, cinnamon (if using), and 3 cups of flour. Switch to the dough hook and mix on low speed. Gradually add the remaining flour, 1/4 cup at a time, until the dough clears the sides of the bowl but remains slightly tacky to the touch.
Knead the dough on medium-low speed for 5 to 7 minutes, or by hand on a floured surface for 10 minutes. The dough should be smooth, elastic, and spring back when poked.
Place the dough in a lightly greased bowl and cover it with a clean kitchen towel or plastic wrap. Let it rise in a warm, draft-free spot for about 60 to 90 minutes, or until it has doubled in size.
Gently punch down the risen dough to release the air. Divide the dough into 15 equal-sized pieces. Roll each piece into a smooth ball and place them in a greased 9×13 inch baking pan.
Cover the pan and let the rolls rise again for 30 to 45 minutes. They should look puffy and be touching each other. Preheat your oven to 350°F (175°C) during this time.
Bake for 18 to 22 minutes, or until the tops are lightly golden brown. Immediately after removing them from the oven, brush the tops with melted butter for a beautiful shine and extra soft crust.