Place tomatoes and ancho peppers in a pot, cover with water, and bring to a boil. Cook until tender, about 5 minutes. Let soak in the hot water for 5 minutes more.
Transfer tomatoes, ancho peppers, and 1/2 cup water into a blender. Cover and hold lid down with a potholder; pulse a few times before leaving on to blend. Strain sauce through a sieve, discarding the solids.
Heat oil in a saucepan over medium heat. Crush garlic with cumin in a bowl and add to the hot pan. Cook and stir until fragrant, about 1 minute. Add mushrooms; cook and stir until soft, about 5 minutes. Pour tomato sauce over the mushrooms and season with salt. Let simmer until sauce is slightly thickened, about 5 minutes. Add vegetable broth. Bring to a boil. Reduce heat and let soup simmer until flavors meld, about 15 minutes.
Pour soup into individual bowls; garnish with onion and oregano. Serve with lime wedges and red pepper flakes on the side.