Bring 2 quarts of water and 1 tablespoon kosher salt to a boil in a large pot; add the noodles and cook according to package directions until al dente.
Reserve at least 1/4 cup of the pasta cooking water, then drain the noodles and set aside.
In a small bowl, whisk together 3 tablespoons vegan oyster sauce, 2 tablespoons cane sugar, 1 tablespoon tamari, 2 teaspoons rice vinegar, and 1 teaspoon sesame oil until smooth.
Heat 2 tablespoons vegan butter in a wok or large skillet over medium-high heat until it sizzles, then reduce to medium.
Add the minced garlic and chopped green onions (reserve half of the green parts for topping) and sauté until the garlic is fragrant and the onions are tender, about 1–2 minutes; avoid browning the garlic.
Pour the sauce mixture into the pan along with 1/2 cup of the reserved noodle water and stir to combine; bring to a simmer and cook for 3 minutes.
Remove the pan from the heat, add the cooked noodles to the sauce, and toss thoroughly to coat, adding more reserved pasta water as needed to reach a silky consistency.
Transfer to serving bowls, top with the reserved chopped green onion greens, and serve hot.