Bring the rice and water to a boil in a saucepan. Reduce heat to medium-low; cover and simmer until the rice is tender and the liquid has been absorbed, 20 to 25 minutes.
Meanwhile, heat a wok or large skillet over medium-high heat. Stir in the garlic and chicken; cook for 2 minutes. Add the fish sauce, oyster sauce, sugar, ginger, red pepper, mushrooms, and onions. Cook and stir until the chicken is no longer pink and the vegetables are nearly tender, about 3 minutes. Dissolve the chile paste in the chicken broth, then add to the chicken mixture. Season to taste with salt and pepper; sprinkle with cilantro leaves to garnish. Serve with the hot rice.