For the Meatballs: Place the rice in a medium bowl and add water to cover, swish the rice with your fingers, and then drain off the water. Repeat until the water runs clear, then cover the rice with room temperature water and set aside for 1-1/2 hours.
Drain the rice briefly, then process, blend or grind (in a mortar) into pieces the size of coarse sand or kosher salt.
Spread the ground lamb or beef over a large cutting board, forming a rectangle about 1/4 inch thick. Scatter the ground rice and onion evenly over the meat, then sprinkle over the black pepper, salt, Marash, and purple basil (or basil and ground anise). With a large chef's knife, work your way horizontally across the meat, rocking the knife and cutting into the ingredients. Turn the cutting board 90 degrees and repeat, again cutting across the meat. Slip the blade of your knife underneath one side of the meat and bring about half of the rectangle up and over the center. Repeat from the opposite side of the meat, and then from the top and bottom. You should now have a small square-ish lump of ground meat. Pat out the meat and repeat the cutting two or three times, until the ingredients are completely mixed into the meat. Gently transfer the meat to a medium bowl.
Put the pumpkin or winter squash in a heavy lidded pot large enough to accommodate it in one or two layers. Sprinkle the salt over the pumpkin.
Place a bowl of water within reach. With wet palms and a very light touch, pinch off tablespoon-sized pieces of the meat mixture, roll them into balls, and lay them on top of the pumpkin pieces; make a second layer if necessary. Handle the meat lightly - don't squeeze or press it when you're forming the meatballs, which needn't be perfectly smooth or round. You should end up with about 26 meatballs.
Stir together the tomato paste and boiling water and pour over the meatballs and pumpkin. Place the pot over high heat and bring the liquid to a boil, then cover, reduce the heat to a slow simmer, and cook until the pumpkin or squash is soft and the meatballs are cooked through, 25 to 35 minutes, depending on the type of squash. There should be a small amount of sauce at the bottom of the pot; check after 15 minutes, and if t here is not sufficient liquid in the bottom of the pot, add 1/4 cup water. Remove from the heat and set aside, covered, while you prepare the spice butter.
Make the Spice Butter: Melt the butter in a small skillet over medium-low hat. When the butter begins to bubble, add the red pepper flakes and purple basil (or basil and ground anise). Swirl or stir the mixture as it sizzles for about 2 minutes, until the spices are very fragrant and darkening but not burning. Pull the skillet from the heat, pour the butter over the meatballs and pumpkin, and serve immediately.
Notes:
PREPARATION TIME: 1-1/4 hours plus 1-1/2 hours for the rice to soak