Heat the vegetable oil in a large pot over medium-high heat. Add the garlic, ginger, and onion and sauté for 2-3 minutes until fragrant.
Add the julienned carrot, red bell pepper, and sliced mushrooms to the pot. Sauté for another 5-7 minutes until the vegetables are tender.
In a separate bowl, whisk together the vegetable broth, soy sauce, rice vinegar, and chili garlic sauce. Pour the mixture into the pot with the vegetables and stir to combine.
In a small bowl, whisk together the cornstarch and 1/4 cup of water until smooth. Add the cornstarch mixture to the pot and stir until the soup thickens.
Slowly pour the beaten egg into the soup while stirring constantly.
Add chopped green onions to the soup and season with salt and pepper to taste.
Serve hot and enjoy!