In a small bowl, whisk together yeast, 1 teaspoon of the sugar, and the warm water. Let stand 5-8 minutes, or until yeast is foamy.

In a large bowl, whisk together the flour, remaining sugar, pumpkin pie spice and salt.

In a medium saucepan, heat the milk and butter over medium low heat until the butter is melted and the mixture is just warm. Do not overheat.

Make a well in the center of the flour mixture, then add the yeast mixture, milk mixture, pumpkin, and eggs. Stir until a soft, batterlike dough forms, 1 to 2 minutes. Transfer dough to a large, lightly greased storage container. Cover and chill overnight.

Remove dough from refrigerator and punch down. Turn onto a well-flour surface. Let rest 10 minutes. Meanwhile, lightly grease two 9x13-inch baking pans. Shape the dough into 24 balls and arrange in the prepared pans (12 per pan). Cover and let rise until doubled in size, about one hour.

Preheat oven to 375 degrees. Whisk together the remaining egg and 1 tablespoon of water. Brush rolls with egg mixture. Sprinkle with rolled oats if desired.

Bake for 20 minutes, or until golden brown. Cool slightly before serving.