In a large pot, combine rinsed rice, chicken broth, ginger slices, and salt. Bring to a boil over high heat, then reduce to low and simmer partially covered.
Cook for 40-45 minutes, stirring occasionally to prevent sticking. The rice should break down and create a creamy, porridge-like consistency. Add more water if it gets too thick.
While congee is cooking, prepare soft-boiled eggs by boiling for 6-7 minutes, then transferring to an ice bath. Peel and set aside.
Remove ginger slices from the congee and stir in sesame oil. Taste and adjust seasoning with more salt if needed.
Ladle congee into bowls and top each with a halved soft-boiled egg, green onions, crispy shallots, and a drizzle of soy sauce. Let everyone add their own favorite toppings at the table!