1. Sprinkle the yeast over the water in a large mixing bowl and stir to dissolve. Using a wooden spoon, beat in the eggs, pumpkin, soft butter, sugar, salt, thyme and cayenne. Add 3 cups of flour and beat until smooth, gradually adding more flour as needed to make a soft, sticky but still manageable dough. Make sure the dough is well mixed. Oil a larger bowl and scrape the dough into it, turning to oil all sides. Cover with a dish towel and let rise in a warm, draft-free spot until doubled in bulk, about 1 1/2 hours. Punch the dough down, cover tightly with plastic wrap and refrigerate overnight.
2. Grease 2 (8-inch) cake pans with melted butter. Punch the dough down again and shape into round dinner rolls, arranging them in pans with about half an inch between each (if the dough is too sticky to handle easily, lightly butter or oil your hands). Cover the rolls with a dish towel and let rise in a warm spot until doubled in bulk, 30 minutes.
3. Heat the oven to 375 degrees. Bake the rolls until browned, 20 to 25 minutes. Serve hot or warm.