Bring water and rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice tender and water has been absorbed, 20 to 25 minutes.

Heat a wok or large skillet over medium-high heat. Add chicken and garlic; cook 2 minutes. Add green onions, bell pepper, mushrooms, ginger, fish sauce, oyster sauce, and sugar; cook and stir until chicken no longer pink and vegetables nearly tender, about 3 minutes. Whisk chili paste into chicken broth in a small bowl until dissolved; add to wok. Season with salt and black pepper. Garnish with cilantro leaves; serve with rice.