Warm the olive oil in a soup pot or Dutch oven over medium heat.
Add the onion and jalapeno and cook for a few minutes until tender. Stir in the garlic, cumin, oregano, salt, and cayenne pepper and cook for one more minute until fragrant. Stir the veggies in the cornstarch until coated.
Add the green chiles, drained and rinsed pinto and navy beans, and vegetable broth to the pot. Increase heat to bring to a boil, then reduce heat to medium-low to maintain a rapid simmer. Let the chili simmer for 15 minutes until thickened. You can use 3 cups instead of 4 cups broth and/or simmer it for longer if you want it to be thicker.
A few minutes before the chili is finished, prepare the sour cream. Place it in a small bowl and add a couple tablespoons of the chili broth. Mix the broth into the sour cream, adding a few more spoonfuls of broth one at a time, until the sour cream is warm. Then, stir this mixture into the chili. This prevents you from adding cold sour cream to hot chili which can cause it to get grainy or lose its creaminess.
Serve the chili with toppings of choice: cilantro, lime juice, tortilla chips, avocado, cheese, more sour cream, onions, jalapeno, or tomatoes. It also goes great with cornbread!
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