Adjust an oven rack to the top position and heat the broiler. Arrange the poblano and Anaheim chiles, skin-side up, on a foil-lined baking sheet and broil until the skins are blackened and blistered, about 5 to 10 minutes.

Transfer the charred peppers to a bowl and cover tightly with plastic wrap; let them steam for 10 minutes so the skins loosen.

Toss the corn kernels with vegetable oil and salt on a baking sheet. Broil until the kernels are spotty brown and charred, about 5 minutes.

Peel and discard the skins from the steamed peppers. Coarsely chop 4 of the poblanos and all of the Anaheim peppers; place the final roasted poblano in a food processor.

Add the onions and jalapeños to the food processor and pulse until they are finely chopped, about 10 pulses, then transfer the mixture to a bowl (no need to wash the processor).

Heat the remaining vegetable oil in a large pot or Dutch oven over medium-high heat. Add the onion and jalapeño mixture and cook until softened and lightly browned, about 5 to 7 minutes.

Stir in the garlic, tomato paste, cumin, and coriander; cook until the spices are fragrant and the tomato paste has darkened slightly.

To the food processor containing the single roasted poblano, add a portion of the cannellini beans and 1 cup of the vegetable broth. Process until the mixture is completely smooth—this creates the thickening base for the chili.

Stir the bean-pepper puree, the remaining cannellini beans, pinto beans, remaining vegetable broth, chopped roasted peppers, and the reserved corn cobs into the pot. Bring to a boil, then reduce the heat and simmer for 20 minutes to allow the flavors to meld and the cobs to release their sweetness.

Remove and discard the corn cobs. Stir in the charred corn kernels, scallions, cilantro, and lime juice. Season with salt and pepper to taste and serve hot.