Adjust an oven rack 6 inches from the broiler element and heat the broiler. Toss the poblanos and Anaheim chiles with oil and arrange them skin-side up on a foil-lined baking sheet. Broil until the skins begin to blacken and soften, about 10 minutes, rotating the pan halfway through. Transfer the chiles to a bowl, cover with plastic wrap, and let them steam until the skins peel off easily, 10 to 15 minutes. Peel the chiles, then cut them into half-inch pieces, reserving any accumulated juice.

Toss the corn kernels with oil and spread them evenly over a foil-lined baking sheet. Broil, stirring occasionally, until the kernels begin to brown, 5 to 10 minutes; set aside to cool.

In a food processor, pulse the onions and jalapeños together until they reach the consistency of chunky salsa, 6 to 8 pulses, then transfer the mixture to a bowl. In the empty food processor, process a portion of the cannellini beans, one cup of the broth, and a portion of the roasted chiles with their juice until 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, 5 to 7 minutes. Stir in the garlic, tomato paste, cumin, coriander, and salt, and 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 bean mixture, the remaining roasted chiles, the remaining cannellini beans, the pinto beans, and the corn cobs. Bring to a simmer, then reduce the heat to low and simmer gently until thickened and flavorful, about 40 minutes.

Discard the corn cobs. Stir in the broiled corn kernels and let them 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.