Combine 1/3 cup rice vinegar and the sliced serrano in a small bowl and let sit at room temperature for at least 15 minutes to make the chili vinegar condiment.
In a bowl, mix the chicken slices with 2 tablespoons water and 1 teaspoon baking soda; let rest at room temperature 15 minutes, then rinse under cold water and drain well.
Bring 6 cups of water to a boil. Place the rice noodles in a large bowl and pour the boiling water over them; stir, then soak until almost tender, about 8 minutes, stirring once halfway. Drain, rinse with cold water, drain again, and toss with 2 teaspoons vegetable oil.
Whisk together 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 in a small bowl; set the sauce aside.
Heat 2 teaspoons oil in a 12-inch nonstick skillet over high heat. Add the sliced garlic and cook, stirring occasionally, until golden brown, 1 to 2 minutes; avoid burning.
Add the drained chicken and 2 tablespoons of the prepared sauce to the skillet. Spread the chicken in an even layer and let it cook without stirring 1 to 1½ minutes until the underside browns. Turn with tongs and cook the second side 1 to 1½ minutes until browned. Push the chicken to one side of the skillet.
Add 2 teaspoons oil to the empty side of the skillet and crack in the eggs; gently stir with a spatula until they begin to set, then combine the eggs with the chicken, breaking the eggs into pieces. Cook another 30 to 60 seconds until eggs are fully set, then transfer the mixture to a bowl.
Wipe the skillet if needed and heat 2 teaspoons oil over high until shimmering. Add the broccolini and 2 tablespoons of the sauce, toss to coat, cover, and cook 2 minutes, stirring once halfway. Uncover and cook 2 to 3 more minutes until browned in spots. Transfer broccolini to the bowl with the chicken and eggs.
Heat 2 teaspoons oil in the skillet and add half the noodles with 2 tablespoons of the sauce; toss and cook about 2 minutes until the noodles begin to brown in spots, stirring only once. Transfer to the bowl with the chicken and broccolini. Repeat with another 2 teaspoons oil, the remaining noodles, and 2 tablespoons sauce.
When the second batch of noodles is starting to brown, return all contents to the skillet, toss to combine, and let cook undisturbed for 1 to 1½ minutes to finish. Serve immediately with the prepared chili vinegar on the side.