Warm a large pot over medium-high heat then add olive oil along with shredded cabbage and carrots; cook, stirring occasionally, until vegetables soften, about 5 minutes.
Pour in soy sauce, brown sugar, ground mustard, ground ginger, and garlic powder, mixing them well with the veggies.
Add the spaghetti noodles (breaking them in half if you prefer) and pour in 3 ½ cups of water, spreading the noodles evenly.
Let the noodles cook uncovered for 15 to 18 minutes, stirring every few minutes once they start to get flexible and more frequently near the end to prevent sticking.
When noodles are tender and cooked through, remove the pot from heat and stir in sesame seeds.
Serve the noodles right away, optionally topping with extra sesame seeds or sliced green onions for garnish.