Cook the noodles according to the package directions until just al dente. Reserve about 1 cup of the starchy pasta water, then drain the noodles.
While the noodles cook, whisk together the soy sauce, vegan oyster sauce, brown sugar, sesame oil, and white pepper in a small bowl.
Melt the vegan butter in a large skillet or wok over medium-low heat. Add the minced garlic and the white parts of the green onions.
Cook for 4 to 5 minutes, stirring frequently, until the garlic is deeply golden and fragrant. Do not let it burn.
Pour the prepared sauce into the skillet and stir. Let it gently bubble for about 30 seconds.
Add the drained noodles and about 1/4 cup of the reserved pasta water. Toss continuously with tongs until the sauce coats the noodles evenly.
Add more pasta water, 1 tablespoon at a time, if needed until the noodles are glossy and well coated.
Taste and adjust the soy sauce or brown sugar if needed. Remove from the heat and top with the sliced green onion tops.
Serve immediately while hot and glossy.