Add warm water (not too hot!!), yeast, and 1 teaspoon of sugar to a large mixing bowl fit for a stand mixer and gently stir together. Let sit for 5 minutes. Yeast should begin to activate and form a layer of foam on top of the water.
While yeast is activating, add milk and 2 tablespoons of unsalted butter to a small sauce pan and scald over medium heat. Scald means to heat right before a simmer. You should see small bubbles form around the edges of the pan. Remove from heat.
Once yeast has activated, add 2 1/2 tablespoons of sugar, 1 teaspoon salt, 1 cup of flour, and egg to the mixture. Stir to combine. Slowly pour in warm milk while stirring into the batter until combined. Let mixture sit for 5 minutes to rest.
Attach bowl to stand mixer and fit mixer with dough hook (you can mix by hand, if you don't have a mixer). Add 1 cup of flour and mix on low to combine. Add another cup and mix to combine. If the dough is still sticking to the edges of the bowl, add 1/2 cup flour. Keep adding if it's still getting stuck to the bowl. One it's not sticking anymore, it's time to knead.
Turn up speed to medium and knead dough for 5 minutes. I like to do this part by hand, instead. If that's what you want to do too, add a little flour to a clean counter and knead dough with the edge of your palms for about 6 minutes. The dough is ready when it's soft and slightly elastic. Place dough ball in a greased bowl and cover with a towel. Let it rise for 1 hour. It should be double in size.
Punch down risen dough and remove from bowl. Place on clean counter with a little sprinkled flour. Cut dough into 3 even slices. Cut each slice into 4 even pieces. You should have 12 even pieces. Roll each piece into a ball, tucking under the edges to form a ball.
Place all the ball into a greased 13 x 9 pan. Cover with a towel and let them rise again for 45 minutes. At the 30-minute mark, preheat oven to 375 degrees.
Remove towel from rolls and bake in preheated oven for 13-15 minutes, or until deep brown on top. Remove from oven and immediately brush with melted salted butter. Serve warm with whipped pumpkin butter (see recipe below).
Leftover rolls can be stored in a plastic storage bag for a couple days or frozen for a month or so. Rolls can be reheated in microwave for 30 seconds.