Heat olive oil and 1 tsp sesame oil in a large pot over medium heat. Add red pepper flakes and cook 1 minute. Add mushrooms and saute until soft and browned. Add garlic and ginger and continue sauteing 1-2 minutes, until fragrant.
Add vegetable broth and 2 cups water. Bring to a boil, then reduce heat and simmer 5 minutes.
Add vinegar, soy sauce, pepper and tofu, and simmer another 3 minutes.
In a small bowl, whisk together remaining ¼ cup water and cornstarch. Add to pot and continue simmering 3 additional minutes, stirring frequently.
Season to taste with salt & cayenne (I like it spicy, so I used about ¼ tsp cayenne).
Slowly stream egg whites into the pot while stirring continuously.
Remove pot from heat and stir in green onions, cilantro, and remaining 1 tsp sesame oil.
Serve immediately.
Recipe by Flying on Jess Fuel at https://www.jessfuel.com/hot-sour-soup/