In a large bowl, whisk warm milk, instant yeast, and granulated sugar. Stir in melted butter, egg, pumpkin puree, and 1 tsp pumpkin pie spice. Add 3 cups flour and salt, mix to a shaggy dough, then knead on a floured surface for 8-10 minutes, adding flour as needed until dough is soft and tacky. Place in a greased bowl, cover, and let rise until doubled, about 1 hour.

Punch dough down and roll into a 16x12-inch rectangle. Spread the 1/4 cup soft butter edge to edge. Mix brown sugar and 2 tsp pumpkin pie spice, sprinkle evenly over butter, and press lightly. Roll up tightly from the long edge and pinch the seam to seal.

Cut the log into 12 even slices and place them cut side up in a buttered 9x13-inch dish. Cover and let rise in a warm spot until puffy and nearly touching, 30 to 45 minutes. Preheat the oven to 350°F (175°C) during the last 15 minutes of rising.

Bake for 22 to 25 minutes until the tops are golden and the centers feel set, tenting with foil if they brown too quickly. Cool in the pan on a wire rack for 10 minutes.

Beat cream cheese, powdered sugar, and maple syrup until smooth. Add enough milk to make a pourable glaze. Drizzle over the warm rolls and serve immediately.