Make the chili vinegar: combine 1/3 cup rice vinegar and the sliced serrano in a small bowl; let sit at room temperature for at least 15 minutes.
Tenderize the chicken: in a bowl, toss the sliced chicken with 2 tablespoons water and 1 teaspoon baking soda; let sit at room temperature for 15 minutes, then rinse with cold water, drain well, and pat dry.
Soak the noodles: bring 6 cups water to a boil, place the noodles in a large bowl, pour the boiling water over them, stir, and soak about 8 minutes until almost tender, stirring once halfway; drain, rinse with cold water, drain well, and toss with 2 teaspoons vegetable oil.
Whisk the sauce: in a small bowl, combine 1/4 cup oyster sauce, 1 tablespoon plus 2 teaspoons soy sauce, 2 tablespoons packed dark brown sugar, 1 tablespoon white vinegar, 1 teaspoon molasses, and 1 teaspoon fish sauce; set aside.
Cook the garlic and chicken: heat 2 teaspoons oil in a 12-inch nonstick skillet over high heat, add the sliced garlic and cook 1–2 minutes until golden but not burned. Add the chicken and 2 tablespoons of the sauce, spread into an even layer, and cook without stirring 1–1½ minutes per side until browned; push the chicken to one side of the skillet.
Scramble the eggs: add 2 teaspoons oil to the empty side of the skillet, pour in the eggs, gently stir until they begin to set, then combine the eggs with the chicken and break into pieces; cook another 30–60 seconds until fully set. Transfer the mixture to a bowl.
Cook the broccolini: heat 2 teaspoons oil in the skillet over high until smoking, add the broccolini and 2 tablespoons sauce, toss to coat, cover and cook 2 minutes (stirring once halfway), then uncover and cook 2–3 minutes more until brown in spots; combine with the chicken and egg mixture.
Fry the noodles in two batches: heat 2 teaspoons oil, add half the noodles and 2 tablespoons sauce, toss and cook about 2 minutes until lightly browned in spots, then transfer to the bowl with the chicken. Repeat with remaining 2 teaspoons oil, noodles, and 2 tablespoons sauce.
Finish the stir-fry: when the second batch of noodles starts to brown, return all contents to the skillet, toss to combine, and leave undisturbed for a final 1–1½ minutes to develop a bit more browning. Serve immediately with the prepared chili vinegar on the side.