Slice the chicken breasts against the grain into thin strips. Prepare the broccolini by cutting the florets into 1-inch pieces and slicing the stalks on the bias into ½-inch pieces. Set aside.
In a large pot, bring water to a boil. Add the rice noodles and soak for about 15–20 minutes until tender but still chewy. Drain and rinse under cold water. Set aside.
In a bowl, combine the chicken slices with baking soda, half of the soy sauce, and a pinch of salt. Marinate for about 15 minutes while preparing the sauce.
Whisk together oyster sauce, remaining soy sauce, dark brown sugar, white vinegar, molasses, and fish sauce in a separate bowl to make the sauce.
Heat 2 tablespoons of vegetable oil in a wok or large skillet over medium-high heat. Add marinated chicken and stir-fry for 3–4 minutes until cooked through and lightly browned. Remove chicken and set aside.
In the same pan, add another tablespoon of oil if needed. Stir-fry sliced garlic and serrano chile for about 30 seconds until fragrant. Add broccolini and stir-fry 2–3 minutes until bright green and tender-crisp.
Return cooked chicken to the pan and add soaked rice noodles. Pour sauce over and toss gently to coat everything well.
Push noodle mixture to one side of the pan. Crack eggs into the empty space and scramble until just set. Mix eggs into the noodle dish.
Remove from heat and serve hot, garnished with extra sliced serrano chiles if desired.