Combine vinegar and serrano chile in small bowl. Set aside at room temperature for at least 15 minutes.
Cut broccolini florets into 1" pieces, and cut stems on bias into 1/2" pieces. If using broccoli, cut florets into 1/2-3/4" pieces; peel stems then slice on bias into 1/2" pieces. You should have about 5 cups. Set aside.
Combine chicken, water and baking soda. Let sit at room temperature for 15 minutes. Rinse chicken and drain well.
Bring 6 c water to a boil. Place noodles in a large bowl. Cover with boiling water. Stir, then let stand 8 minutes exactly, stirring once halfway through. Drain well, rinse with cold water and toss with 2 t oil.
Whisk oyster sauce, soy sauce, brown sugar, vinegar, molasses and fish sauce together in a bowl.
Heat 2 t oil and garlic in large nonstick skillet over high heat, stirring occasionally, until deep golden brown (much darker than typical for American/European dishes), 1-2 minutes. Add chicken and 2 T sauce mixture. Toss to coat and spread chicken out into an even layer. Cook without stirring until chicken begins to brown, 60-90 seconds. Flip chicken pieces with tongs and cook without stirring until second side begins to brown, another 60-90 seconds. Push chicken to one side of skillet.
Add 2 t oil to clear area of skillet. Add eggs to oil. Using rubber spatula, stir eggs gently until set but not dry. Stir eggs into chicken and cook, tossing to break up large clumps of egg, until egg is cooked through, another 30-60 seconds. Transfer to a clean bowl.
Add 2 t oil to empty skillet and heat over high heat until smoking. Add broccolini (or broccoli) and 2 T sauce. Toss to coat, cover skillet, and cook 2 minutes, stirring once halfway through. Remove lid and cook without more stirring until crisp-tender and very brown in spots, 2-3 minutes. Add vegetable to chicken in bowl.
Again heat 2 t oil in empty skillet until smoking. Add half of noodles and 2 T sauce. Toss to coat and cook until noodles are starting to brown in spots, about 2 minutes, stirring halfway through. Add to bowl.
Repeat previous step with remaining oil, remaining noodles and remaining sauce. When second batch of noodles are brown, add contents of bowl back to skillet and toss to combine. Cook without stirring until everything is hot, 1-2 minutes. Serve at once, passing chile vinegar alongside.