Warm the milk to 105-110°F (40-43°C). If using active dry yeast, stir the milk, yeast, and brown sugar together and let the mixture stand for 5-10 minutes until slightly foamy; instant yeast may be mixed directly with the flour.

Add the pumpkin purée, egg, butter, salt, cinnamon, ginger, and nutmeg to the milk mixture. Stir until the wet ingredients and spices are evenly combined.

Mix in about 3 1/2 cups flour gradually. Knead for 6-8 minutes in a mixer or 8-10 minutes by hand, adding only enough of the remaining flour to create a soft, slightly tacky dough.

Place the dough in a lightly greased bowl, cover it, and let it rise in a warm, draft-free spot for 60-90 minutes, or until doubled in size.

Deflate the risen dough and divide it into 12-15 equal pieces. Shape each piece into a smooth ball and arrange the balls in a greased 9-by-13-inch pan or two round pans.

Cover the shaped rolls and let them rise for another 30-45 minutes, until noticeably puffy. Meanwhile, heat the oven to 350°F (175°C).

Bake the rolls for 20-25 minutes, until lightly golden and the center rolls reach approximately 190°F (88°C). Brush the hot rolls with melted butter and add pumpkin seeds or flaky salt if desired.