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.

For round dinner rolls, grease 2 (8-inch) cake pans with melted butter. Punch the dough down again and shape into round rolls, arranging them in pans with about one-half inch between each. For cloverleaf rolls, butter a 12-cup muffin tin, tear off tablespoon-sized balls and place 3 in each muffin cup. (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, about 30 minutes.

Heat the oven to 190 degrees. Bake the rolls until browned, 20 to 25 minutes. Serve hot or warm.