In a blender, place one can of the drained white beans and 1 cup of the broth and blend until smooth. Set aside.

Heat the olive oil in a large pot or Dutch oven over medium heat. Add the onion, poblano, salt, and several grinds of pepper, and cook for 5 minutes, stirring occasionally, or until softened. Stir in the green chiles, garlic, cumin, oregano, and coriander, and cook, stirring, for 30 seconds. Add the remaining 2 cups broth and 2 cans drained white beans. Simmer for 10 minutes.

Add the bean puree, stir, and simmer, uncovered, for 25 to 35 minutes, stirring occasionally, until thickened. Remove from the heat, let sit for 10 minutes to continue to thicken, then stir in the lime juice. Season to taste and serve with desired toppings and lime wedges for squeezing.