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1
Combine 1/3 c vinegar and thai chile in bowl. Let stand at room temperature for at least 15 minutes.
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2
Combine chicken with 2 tablespoons water and baking soda in bowl. Let sit at room temperature for 15 minutes. Rinse in cold water and drain.
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3
Prepare noodles. Drain well and toss with 2 teaspoons oil.
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4
Heat 2 teaspoons oil and garlic in nonstick skillet over high heat, stirring occasionally, until garlic is deep golden brown, 1 to 2 minutes. Add chicken and 2 tablespoons sauce mixture, toss to coat, and spread chicken into even layer. Cook, without stirring, until chicken begins to brown, 1 to 11/2 minutes. Flip chicken and cook, without stirring, until second side begins to brown, 1 to 11/2 minutes. Push chicken to 1 side of skillet. Add 2 teaspoons oil to cleared side of skillet. Add eggs to clearing. and stir gently until set but still wet. Stir eggs into chicken and continue to cook, breaking up large pieces of egg, until eggs are fully cooked, 30 to 60 seconds. Transfer mixture to bowl.
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5
Heat 2 teaspoons oil in now-empty skillet until smoking. Add broccolini and 2 tablespoons sauce and toss to coat. Cover and cook for 2 minutes, stirring once halfway through cooking. Remove lid and continue to cook until broccolini is crisp and very brown in spots, 2 to 3 minutes, stirring once halfway through cooking. Transfer broccolini to bowl with chicken mixture.
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6
Heat 2 teaspoons oil in now-empty skillet until smoking. Add half of noodles and 2 tablespoons sauce and toss to coat. Cook until noodles are starting to brown in spots, about 2 minutes, stirring halfway through cooking. Transfer noodles to bowl with chicken mixture.
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7
Repeat with remaining 2 teaspoons oil, noodles, and sauce. When second batch of noodles is cooked, add contents of bowl back to skillet and toss to combine. Cook, without stirring, until everything is warmed through, 1 to 11/2 minutes. Transfer to platter and serve immediately, passing chile vinegar separately.
