In the bowl of a stand mixer, whisk the water and yeast together until bubbly and then allow it to sit for 1 minute. Add the butter, sugar, pumpkin puree and eggs and whisk until just combined.
Attach the dough hook to the mixer. Stir the salt and pumpkin pie spice into the flour and then add them to the mixer on low speed.
Allow the dough to mix for approximately 5 minutes on low speed. It will be sticky. If it's not coming together, add up to 4 more tablespoons of flour, adding 1-2 tablespoons at a time. You can also put a small amount of vegetable oil on your hands to keep the dough from sticking to them.
Place the dough in a lightly greased large bowl and cover. Allow to double in size, approximately 1 hour.
Preheat the oven to 350 degreesF and lightly grease 2 8-inch cake pans. Divide the dough into 10 equal sized balls and place 5 in each cake pan. Allow the dough to rise for another 25-30 minutes.
Bake for 20 minutes or until fully cooked through. Serve warm.
Homemade Pumpkin Pie Spice (yields more than needed for this recipe)