Before prepping any other ingredients, soak dried mushrooms in 1 ½ cups hot, but not boiling, water.
Prepare all the ingredients while the mushrooms soak.
When the mushrooms have soaked at least 10 minutes, add them into a high-speed blender with the nutritional yeast. Blend on low for 30 seconds, then on high for 2-3 minutes, until evenly blended and smooth. If any solid pieces of mushroom stick to the sides of the blender, slowly add a bit more water.
Heat the olive oil in a large, heavy pot over medium heat.
When the oil is hot, add the onion, carrot, tomato paste, and salt. Saute for 3 minutes, stirring occasionally, until onions are slightly translucent.
Add garlic. Saute 2 more minutes, stirring.
Add chile powder, paprika, and cumin. Saute for 2 minutes.
Add sherry. Use spatula to scrape any stuck bits from the pot.
Add 2 cups of the vegetable stock, the fresh mushrooms, the canned tomatoes, and the blended mushrooms and nutritional yeast. Stir.
When the liquid starts to boil, reduce to a simmer. Stir again to ensure there is no scorching on the bottom of the pot. Add more vegetable stock if the consistency is too thick. The chili should be slightly runny at this point.
Add chickpeas. Stir. Continue to simmer over medium-low heat for 10-15 minutes, still stirring, until chili reaches desired consistency.
If using vegan chorizo: heat the remaining 2 tablespoons of olive oil in a medium skillet over medium heat. When the oil is hot, add the chorizo, spreading it into an even layer across the skillet. Wait 2-3 minutes before stirring, so the chorizo is browned. Continue to brown like this twice more, until the chorizo is heated through and has been browned three times.
Serve the chili in bowls. Top with some chorizo, a sprinkle of vegan cheese, and some green onion.