Combine pork shoulder and liver in a large saucepan. Add 4 cups water and bring to a boil over medium-high heat. Reduce the heat to medium-low, cover, and simmer until pork is tender, about 1 1/2 hours.

Meanwhile, bring remaining 4 cups water and rice to a boil in a saucepan. Reduce the heat to medium-low, cover, and simmer until rice is tender and liquid has been absorbed, 20 to 25 minutes. Set aside.

Use a slotted spoon to transfer pork to a cutting board; let cool.

Stir green onions, onion, parsley, bell pepper, celery, cilantro, and garlic into the simmering pork broth. Season with salt, cayenne pepper, black pepper, and pepper flakes. Simmer until onion is tender, 5 to 7 minutes.

Meanwhile, grind cooled meat using the coarse plate of a meat grinder. Stir ground meat into the vegetable mixture and cook, stirring frequently, until the liquid has nearly evaporated, about 10 minutes. Stir in cooked rice and set aside to cool.

While the meat mixture is cooling, rinse sausage casings inside and out with plenty of warm water. Keep casings in a bowl of warm water until ready to stuff.

Once the sausage mixture is cool enough to handle, stuff into the prepared casings using a sausage stuffer. Prick sausages with a needle every 4 to 6 inches.

Bring a large pot of salted water to a boil over high heat. Reduce the heat to keep the water at a gentle simmer. Add sausages and cook gently until hot on the inside, firm to the touch, and plumped in appearance, about 5 minutes. Serve immediately.