Make the scallion chili sesame oil. In a small bowl, combine the sesame oil, chili paste, and scallions.
Make the ramen. Add the sesame oil to a large saucepan over medium heat. Once the oil is glistening, add the garlic and ginger and cook, stirring, until fragrant, 1 minute.
Add the chicken stock, soy sauce, scallions, mushrooms, chicken, and salt and bring to a boil over high heat. Add the ramen noodles and boil, stirring occasionally, until soft, about 3 minutes.
To serve, divide the ramen into 2 bowls. Top with the egg halves, drizzle with the scallion oil and sprinkle with sesame seeds, if using.