**Activate the Yeast:** In a small bowl, combine warm milk, yeast, and 1 tablespoon of sugar. Let sit for 5–10 minutes until frothy.

**Mix the Dough:** In a large bowl or stand mixer, mix the pumpkin puree, melted butter, egg, vanilla extract, remaining sugar, and yeast mixture. Gradually add the flour, salt, cinnamon, and nutmeg. Knead until a soft, slightly sticky dough forms.

**First Rise:** Place the dough in a lightly greased bowl, cover with a clean towel, and let rise in a warm place for about 1 hour, or until doubled in size.

**Prepare the Filling:** In a small bowl, mix the softened butter, brown sugar, cinnamon, and ginger until combined.

**Shape the Rolls:** On a floured surface, roll out the dough into a 16x12-inch rectangle. Spread the filling evenly over the dough, leaving a small border. Roll tightly from the long edge into a log, then cut into 12 even pieces.

**Second Rise:** Arrange the rolls in a greased 9x13-inch baking dish. Cover and let rise for another 30–40 minutes.

**Bake:** Preheat the oven to 350°F (175°C). Bake the rolls for 20–25 minutes, or until golden brown.

**Glaze:** Whisk together powdered sugar, milk, and vanilla extract. Drizzle over warm rolls before serving.