Rinse the jasmine rice under cold water until the water runs clear. Drain well.
In a large pot, combine the rinsed rice and chicken broth. Bring to a boil over medium-high heat.
Once boiling, reduce the heat to low and add the shredded chicken, ginger, garlic, soy sauce, salt, and black pepper.
Cover the pot and let it simmer for about 30-40 minutes, stirring occasionally, until the rice has broken down and the congee reaches a creamy consistency.
If the congee is too thick, add additional chicken broth or water to reach your desired consistency.
Stir in the sesame oil and adjust seasoning if needed.
Serve hot, garnished with sliced green onions, cilantro, and fried shallots if desired.