In a large skillet, heat the oils until shimmering. Add the onion and celery and cook, stirring, until tender, about 3 to 5 minutes.
Add the cole slaw mix, and continue to cook, stirring, until the cabbage is wilted and the onions have started to turn clear, about 5 to 7 minutes more.
Cook the pasta in a large pot of boiling salted water. Cook just until al dente.
Meanwhile, combine the soy sauce and the brown sugar in a small dish, and stir until the brown sugar is dissolved.
Rinse and drain the pasta and return it to the pot on low. Add the soy sauce mixture and the sautéed vegetables. Cook, tossing to combine the noodles with the soy sauce and vegetables. Serve immediately.
Note: leftovers are good for up to 4 days in the refrigerator.