Heat the olive oil in a large heavy-bottomed pot over medium-high heat until shimmering. Add the mushrooms, carrots, bell pepper, 1 teaspoon salt and a few grinds of pepper and cook, stirring occasionally, until the vegetables are softened, 4 to 5 minutes. Add the garlic, ginger and scallion whites and cook, stirring, until softened, 2 to 3 minutes. Add the pork, 1 teaspoon salt and a few grinds of pepper and cook, breaking up the pork with a spoon and stirring occasionally, until no longer pink, 5 to 6 minutes.
Pour in the chicken broth and bring to a boil. Add the noodles and cabbage and cook until the noodles are tender and cooked through and the cabbage is tender but still holds a bit of crunch, about 6 minutes. Stir in the soy sauce and vinegar to combine. Season with salt and pepper.
Ladle the soup into bowls, sprinkle with the scallion greens and top with some sesame seeds and sriracha if desired.
