Pumpkin-enriched yeast dough swirls around a cinnamon-sugar filling; cream cheese frosting cloaks the top of each of these Pumpkin Cinnamon Rolls.
Lightly brush a large bowl with butter; set aside. Heat milk and 3 tablespoons butter in a small saucepan over medium heat until butter is melted and mixture is warm to the touch, about 120 degrees. Transfer to the bowl of a stand mixer fitted with the dough hook attachment. Immediately sprinkle with yeast. Let stand until a bit foamy, about 5 minutes. Add flour, granulated sugar, egg, pumpkin, and 1 teaspoon salt. Mix on medium-low speed, scraping sides and bottom of bowl once, until dough is smooth and elastic, about 7 minutes. Transfer to bowl and cover tightly with plastic wrap. Let rise in a warm place until doubled in size, about 1 to 2 hours.
Brush a 9-by-13 baking dish with butter; set aside. In a medium bowl, stir together remaining stick butter, brown sugar, cinnamon, and a large pinch of salt until smooth and fluffy. Set aside.
Transfer dough to a lightly floured work surface. Roll out to 15- by-12-inch rectangle. Spread butter mixture over dough, leaving 1/4-inch border. Starting at a long edge, roll up dough like a jelly roll, then cut crosswise into 15 pieces. Place pieces in pan cut-side up, spaced evenly. Cover tightly with plastic wrap and let rise in a warm place until buns are almost doubled in size, about 45 minutes to 1 hour.
Preheat oven to 350 degrees. Bake buns until golden brown and topping is bubbling around sides of pan, about 17 to 20 minutes. Let cool in pan on a wire rack 10 minutes.
Meanwhile, in the bowl of an electric mixer fitted with the paddle attachment, beat cream cheese on medium-high speed until light and fluffy, 2 minutes, scraping down sides of bowl as needed. Add confectioners' sugar, a pinch of salt, and 2 tablespoons milk and beat until combined, about 1 minute. If glaze is too thick to drizzle, add more milk, 1 teaspoon at a time. Spread half the glaze over slightly cooled rolls. Serve warm or room temperature with additional glaze if desired.