Heat the vegetable oil in a large pot over medium heat. Add all but a few tablespoons of the chopped red onion. Stir in the garlic, chili powder and cumin and cook, stirring occasionally, until the onion begins to soften, about 3 minutes. Add the poblano, mushrooms and corn and cook, stirring occasionally, until just tender, about 3 more minutes. Add the beans, tomatoes, 1 1/2 cups water and 1/2 teaspoon each salt and pepper. Bring to a boil, then stir and reduce the heat to medium. Simmer, stirring occasionally, until the vegetables are tender and the chili is thick, about 20 minutes. Season with salt and pepper.
Divide the chili among bowls. Top with the cheese, sour cream and/or cilantro; sprinkle with the reserved red onion. Serve with the tortillas.