Prep ingredients: Bring a large pot of salted water to a boil. Peel and finely chop 2 teaspoons of garlic. Peel and finely chop 1 tablespoon ginger. Trim scallions, then thinly slice. Slice Chinese broccoli crosswise into 1-inch pieces. Coarsely chop cilantro leaves and stems together. Pat chicken dry, then cut into 1-inch pieces; season with salt and pepper.

Cook chicken & broccoli: Heat 1 tablespoon oil in a large skillet over medium-high. Add chicken and cook, without stirring, until well browned on one side, about 3 minutes. Add Chinese broccoli and cook, stirring chicken and broccoli occasionally, until chicken is cooked through and broccoli is crisp-tender, 2–3 minutes more. Transfer to a plate. Wipe out the skillet.

Cook aromatics: Heat 1 tablespoon oil in the same skillet over medium-high. Add chopped garlic and ginger, and sliced scallions. Cook, stirring, until fragrant, 1–2 minutes. Transfer to a bowl.

Make caramel sauce: In the same skillet, stir to combine ¼ cup sugar and 2 tablespoons water. Cook, without stirring, over medium-high until sugar is melted. Continue to cook, swirling the skillet, until sugar becomes honey-colored, 2–5 minutes (watch closely). Add 2 tablespoons black-bean garlic sauce and ¾ cup water; swirl (don't stir) to combine (caramel may harden, but will melt over heat).

Simmer sauce: Bring sauce to a simmer, then add garlic, scallion, and ginger mixture to skillet. Continue to simmer until the sauce is slightly thickened and glossy, about 3 minutes more. Meanwhile, add noodles to boiling water, cook, stirring occasionally to prevent sticking, until just tender, 6-8 minutes. Drain noodles and rinse under warm water

Finish & serve: Add noodles, chicken, and Chinese broccoli to caramel sauce. Cook over high heat, tossing constantly to combine, until noodles have absorbed most of the sauce and chicken is heated through, about 3 minutes. Serve noodles topped with cilantro and a drizzle of Sriracha, if desired.