Cut lamb spare ribs into 1 or 2 segments. Prepare vegetables.
Heat oil in a wok over medium high heat until warm. Add garlic and ginger. Stir a few times until fragrant.
Carefully add lamb ribs and let them cook without stirring for 1 minute. Stir and cook for 1 minute. Add 1 teaspoon salt. Stir and cook until the surface of ribs is cooked and turns golden brown, about 3 minutes.
Add onion, stir to mix well, for 1 minute. Add carrot. Stir and cook for 2 to 3 minutes.
Add 3 cups water. Cook until brought to a boil. Skim brown foam from the surface. Add sugar, cumin powder, and chili peppers. Place Sichuan peppercorn in a tea infuser and add it into the wok. Bring to a boil again, then turn to low heat and cover. Cook for 1 hour 30 minutes. During cooking, check on the lamb 3 to 4 times. After 1 hour, add the remaining 1 teaspoon salt. If the water is reducing quickly and no longer covers the lamb, carefully add just enough hot water to cover.
Forty minutes before the lamb is ready, prepare the rice. Rinse rice 2 to 3 times. Cover with water and let soak for 30 minutes. Drain and set aside.
When the lamb is ready, use a spatula to push the lamb to the edges of the wok and leave some room in the center. Add rice to fill the space. If the water doesn’t cover the rice completely, add more hot water, about 1/2 to 1 cup. Cover the wok and cook over medium heat for 5 minutes. Uncover, stir, and continue cooking until the water is almost absorbed, about 5 minutes.
Transfer everything to a large dutch oven (or a big pot with a thick bottom). Cover and simmer over lowest heat for 25 minutes.