Heat olive oil in a large pot over medium heat. Add the onions and cook for 2 minutes, stirring frequently until softened. Add the garlic, cumin, oregano, chili powder, and black pepper, then continue cooking for an additional 30 seconds.
Add the cannellini beans, Great Northern beans, corn, and green chiles. Pour in the vegan chicken-style broth and give it a good stir to combine ingredients.
Bring just to a boil, then reduce the heat to low. Cover and simmer for 30 minutes, stirring occasionally.
Stir in the cream cheese and continue cooking, uncovered for 15 minutes, until the chili is slightly thickened and creamy.
Adjust seasoning to taste, sprinkle with cilantro and toppings of choice. Serve hot.