Heat oil in a Dutch oven or pot over medium. Add shallot and sauté until starting to brown, about 5 minutes.
Add rice, and cook 2 minutes. Stir in garlic, ginger, and 8 cups water; season with 1 teaspoon salt and bring to a boil. Reduce heat to medium-low and simmer, uncovered, stirring occasionally, until rice has started to swell 8–10 minutes.
Add sweet potatoes and simmer over medium-low heat, uncovered, stirring occasionally, until soup is thickened and potatoes and rice are tender, 15 minutes. Add chicken and cook until heated through, 2 minutes. Stir in lime juice, soy sauce and oyster sauce; season with salt to taste.
Divide soup among bowls. Top with cilantro, a drizzle of toasted sesame oil, and black pepper.
Store leftover soup in an airtight container in the refrigerator. Reheat soup over medium-low, adding water to thin as needed.