Adjust an oven rack to 6 inches from the broiler element and heat the broiler. Toss the poblanos and Anaheims with a portion of the oil and arrange them skin-side up on an aluminum foil-lined baking sheet. Broil until the skins blacken and the chiles soften, about 10 minutes, rotating the pan halfway through. Transfer the chiles to a bowl, cover with plastic wrap, and let them steam for 10 to 15 minutes; once cool enough to handle, peel the skins and cut the chiles into half-inch pieces, reserving any accumulated juice.

Toss the corn kernels with another portion of oil, spread them over a foil-lined baking sheet, and broil until they begin to brown and smell toasted, about 5 to 10 minutes, then let them cool on the sheet.

Pulse the onions and jalapeños in a food processor to the consistency of chunky salsa, about 6 to 8 pulses, then transfer to a bowl. In the same processor, blend a portion of the cannellini beans, a portion of the broth, and a portion of the chopped roasted chiles with their juices until the mixture is completely smooth, about 45 seconds.

Heat the remaining oil in a Dutch oven over medium heat until shimmering. Add the onion-jalapeño mixture and cook until softened, about 5 to 7 minutes. Stir in the garlic, tomato paste, cumin, coriander, and salt; cook until the tomato paste begins to darken, about 2 minutes.

Pour in the remaining broth, scraping up any browned bits from the bottom of the pot. Stir in the pureed chile-bean mixture, the remaining roasted chiles, the rest of the cannellini beans, the pinto beans, and the corn cobs. Bring to a simmer, then reduce the heat to low and cook gently until the chili has thickened and the flavors have developed, about 40 minutes.

Discard the corn cobs. Stir in the broiled corn kernels and let heat through for 1 minute. Remove from the heat and stir in the scallions, cilantro, and lime juice. Season with salt and pepper to taste and serve hot.