What You Need
Preheat a 12" or 14" Hybrid Wok over high heat for at least 2 minutes. Add the oil and swirl to coat the wok. Once oil is shimmering, crack the egg into the work. Stir lightly, breaking up the yolk and white, until just cooked, about 10 seconds.
Add the meat or other protein and cook, stirring occasionally, until opaque but not cooked throughout, about 1 minute.
Add the garlic and fermented soy bean paste to the wok and stir to combine, then add the noodles. Cook, stirring the noodles a couple times, just so they are separated and not crowded, until the meat and noodles begin to brown, about 2 minutes (If the noodles are browning too quickly, pull the wok off the heat briefly; do not turn the heat down.)
Pour the vinegar around the rim of the wok and cook, stirring, until the vinegar has evaporated. (This should happen pretty quickly.) Add the sugar, soy sauces, and oyster sauce and cook, stirring occasionally until the sauce begins to caramelize, about 1 minute.
Add the broccoli and cook, stirring a few times, until the stems are crisp-tender and the leaves are wilted, about 1 minute more. Serve topped with a pinch of white pepper and sliced chili peppers.