**1. Make the Dough:**
- In a large bowl, combine flour, sugar, yeast, and salt.
- In a separate bowl, whisk together warm milk, melted butter, pumpkin puree, and egg. Gradually add the wet ingredients to the dry ingredients, mixing until a soft dough forms.
- Knead the dough on a floured surface for 5-7 minutes until smooth and elastic, or use a stand mixer with a dough hook for 3-4 minutes.
- Place the dough in a lightly greased bowl, cover, and let rise in a warm place for 1 hour, or until doubled in size.
**2. Prepare the Filling:**
- In a small bowl, mix pumpkin puree, brown sugar, cinnamon, nutmeg, and ginger until smooth.
**3. Roll and Fill:**
- Roll the dough into a rectangle (about 12x18 inches) on a floured surface. Spread softened butter over the dough, then evenly spread the pumpkin filling on top.
- Roll the dough tightly from the long side into a log. Slice into 12 equal pieces.
**4. Arrange and Rise:**
- Place the rolls in a greased 9x13-inch baking dish. Cover and let rise for 30 minutes, or until puffed.
**5. Bake:**
- Preheat the oven to 350°F (175°C). Bake the rolls for 20-25 minutes, or until lightly golden.
**6. Make the Glaze:**
- In a medium bowl, beat cream cheese and butter until smooth. Add powdered sugar, vanilla, and milk, mixing until you reach your desired consistency.
**7. Glaze and Serve:**
- Spread the cream cheese glaze over warm cinnamon rolls. Serve immediately.