Heat the oil in a large pot over medium heat. Add the sliced shallot and cook for 4 to 5 minutes, stirring occasionally, until softened.
Add the garlic, ginger, brown sugar, and mushrooms. Cook for 2 to 3 minutes, stirring often, until fragrant and the mushrooms begin to soften.
Stir in the soy sauce, chicken broth, and water. Increase the heat and bring the soup to a gentle boil.
Add the noodles and cook for 2 to 3 minutes.
Add the frozen wontons and continue cooking for another 2 to 3 minutes, or until the wontons are heated through and the noodles are tender.
Turn off the heat and stir in the chopped green onions.
Taste the broth and add a little more soy sauce if needed. Serve hot with chili oil or red pepper flakes on top, if using.
