For the porridge:
1 (2-pound) pumpkin, kabocha, or butternut squash, peeled and cut into 1-inch cubes
4 cups water
1/4 cup sweet rice flour
1/4 cup brown sugar (or to taste)
1 teaspoon salt
1/2 cup cooked red beans (optional)
2 tablespoons pine nuts (optional)
1 teaspoon black sesame seeds (optional)
For the sweet rice dumplings:
1/2 cup sweet rice flour
3 to 5 tablespoons hot water
To prepare the porridge, fill a saucepan with an inch or two of water. Place a steamer basket or colander in the saucepan, cover, and bring to a boil over high heat. Place the pumpkin in the basket, cover, and reduce heat to medium. Make sure the water doesn't boil away; if necessary, add more water during steaming. Cook the pumpkin until very tender when pierced with the tip of a knife, about 20 minutes.
While the pumpkin steams, prepare the rice balls. In a bowl, combine 1/2 cup sweet rice flour and 3 tablespoons of hot water. Using your hands, knead it to form a dough. The dough should be soft and pliable like play-dough — not too dry and not too sticky. If necessary, add more water, a little at a time, to reach the right consistency.
Divide the dough into 12 pieces and roll into balls. Keep the balls covered with a damp towel to prevent them from drying out. Set aside.
Transfer the pumpkin to a blender along with 4 cups water, 1/4 cup sweet rice flour, and the brown sugar and salt. Blend until smooth. Pour into a saucepan and simmer over medium heat for 5 minutes, stirring frequently.
While the porridge simmers, cook the rice balls. Bring a medium saucepan of water to a rolling boil. Add the rice balls and cook until they float, about 2 minutes. Use a small strainer or slotted spoon to remove the cooked dumplings.
If using red beans, add a spoonful of beans to the bottom of each individual bowl. Ladle the porridge into the bowls. Add three rice dumplings to each bowl. Garnish with pine nuts and sesame seeds, if using. Serve immediately.