Step 1

Combine chiles and vinegar in a glass jar, cover tightly, and chill at least 2 day before using.Do ahead: Chiles can be pickled 2 months ahead. Keep chilled.

Step 2

Toast chiles in a dry small skillet over low heat until brittle and slightly darker in color but not browned and blistered, about 4 minutes. Transfer to a plate and let cool. Grind in spice mill or with mortar and pestle to the consistency of coarse cornmeal.Do ahead: Chiles can be ground 6 months ahead. Store airtight in a cool, dry place.

Step 3

If using dried rice noodles, bring a large pot of water to a boil. Add noodles and stir to separate and prevent sticking, then remove pot from heat. Let noodles sit until cooked through and no hard center remains, 8–10 minutes. Drain in a colander and rinse under cold running water until cool. Drain well again; set aside.

Step 4

Trim about 1" off bottom of each broccoli stem. Remove stalks from tops and slice on a diagonal ¼" thick; set aside. If using chinese broccoli, cut tops into 2" pieces. If using broccoli, cut into 2" florets. Set aside, keeping separate from stalks.

Step 5

Heat oil in a wok or a large nonstick skillet over high until shimmering. Crack eggs into pan; add garlic and cook, stirring, until eggs are almost set. Add broccoli stalks and chicken and cook, tossing often, until chicken is cooked through, about 2 minutes.

Step 6

Add dark sweet soy sauce, thin soy sauce, vinegar, soy bean paste, ½ tsp. sugar, reserved noodles, and reserved broccoli florets, if using regular broccoli, and cook, stirring, until noodles absorb some of the sauce and are softened, about 1 minute. Continue to cook, undisturbed, until underside starts to brown and more sauce has been absorbed, about 1 minute. Turn noodles over and cook, undisturbed, until underside is browned, about 2 minutes. Add Chinese broccoli, if using, and cook, tossing, until bright green, about 2 minutes.

Step 7

Divide noodles among plates and season with white pepper. Serve with fish sauce, pickled chiles, chile powder, and more sugar alongside for topping as desired.