Preheat the oven: Preheat oven to 375°F (190°C). Grease a 9-inch round or square baking dish.
Mix dry ingredients: Whisk flour, sugar, baking powder, baking soda, salt, cinnamon, nutmeg, ginger, and cloves in a large bowl.
Mix wet ingredients: In another bowl, whisk pumpkin puree, buttermilk, melted butter, and vanilla.
Make the dough: Add the wet ingredients to the dry ingredients and gently stir until a soft dough forms. Don't overmix.
Roll out: Transfer the dough to a lightly floured surface and gently bring it together. Roll into approximately a 12×16-inch rectangle.
Add filling: Spread softened butter over the dough. Mix brown sugar, cinnamon, and pumpkin pie spice, then sprinkle evenly over the butter.
Roll: Starting from one long side, roll the dough into a log. Cut into 9–12 equal pieces.
Arrange: Place the rolls cut-side up in the prepared baking dish.
Bake: Bake for 22–28 minutes, until lightly golden and cooked through.
Make glaze: Whisk powdered sugar, milk, and vanilla until smooth.
Finish: Cool the rolls for 5–10 minutes, then drizzle with glaze and serve warm.