Add the oyster sauce, brown sugar, soy sauce and sesame oil to a bowl and stir until combined.
Bring a large pot of water to a boil and cook the noodles according to the package directions (boil for 7-10 minutes). Drain the cooked noodles in a colander, then set aside.
While the pasta cooks, mince the garlic and slice the green onions. Melt the butter in a large skillet over medium-low heat. Once the butter is melted and bubbly, add the garlic and onions (save a few for garnish) and sauté until they are soft and fragrant (1-2 minutes).
Remove the skillet from the heat. Add the drained pasta and oyster sauce mixture to the skillet, and stir well to coat the pasta. If your pasta is stiff or sticky making it hard to stir, sprinkle a small amount of hot water over the pasta to loosen it up. Garnish the pasta with any reserved sliced green onions, then serve.
*Oyster saucecan be found in the International aisle of most major grocery stores (look near hoisin sauce). If you can't find it, it's worth it to seek out an Asian market, where oyster sauce is likely to be much less expensive than in chain grocery stores. I personally feel that the salty, rich flavor of the oyster sauce makes this dish what it is, and I wouldn't suggest substituting it. That being said, several readers have said they've used hoisin sauce, which is much sweeter, and have enjoyed the results. **Feel free to reduce the amount of sugar used by half if you want a more savory sauce.***I love the delicate texture of angel hair pasta in this recipe. However, you can try another long pasta like spaghetti or use rice noodles.