Bloom the Yeast: In the bowl of a stand mixer, whisk together warm milk, yeast, and 1 tablespoon of granulated sugar. Let sit for 5 to 7 minutes until frothy and bubbly.

Mix the Dough: Add the remaining sugar, pumpkin purée, melted butter, egg, and vanilla. Using the dough hook attachment, gradually mix in flour, pumpkin pie spice, and sea salt on low speed until a shaggy dough forms. Knead on medium-low speed for 7 to 8 minutes until smooth, elastic, and slightly tacky but not sticking to your fingers.

First Rise: Shape dough into a ball and place in a lightly greased bowl. Cover with a damp towel and let rise in a warm spot for 60 to 75 minutes until doubled in size.

Roll and Fill: Punch down dough and roll out on a lightly floured surface into a 12x18-inch rectangle. Spread softened butter evenly over the dough leaving a 1/2-inch border. Whisk brown sugar, cinnamon, and pumpkin pie spice together and sprinkle generously over butter, pressing lightly into the dough.

Slice into Rolls: Roll the dough tightly from the long edge into an 18-inch log. Using unflavored dental floss or a sharp serrated knife, slice into 12 equal rolls (approx. 1.5 inches each). Arrange in a buttered 9x13-inch ceramic baking dish.

Second Rise: Cover baking dish loosely and let rolls rise for 35 to 45 minutes until puffed and touching.

Bake to Golden Perfection: Preheat oven to 350°F (175°C). Bake rolls uncovered for 22 to 26 minutes until edges are lightly golden and center rolls register 190°F internally.

Frost and Serve Warm: While rolls bake, beat cream cheese, butter, powdered sugar, vanilla, and milk until silky and fluffy. Spread half the frosting over the rolls while warm so it melts into every cinnamon crevice. Let cool 10 minutes, spread remaining frosting, and serve warm!