Char the poblanos by placing them directly on the flames of a gas burner, turning occasionally, until blackened on all sides. (If you don't have gas burners, you can char them under the broiler or on a grill.) Place charred poblanos into a large bowl, top bowl with plastic wrap or a plate that fits tightly, and let the poblanos steam until they're relatively cool. Then, using a damp paper towel or your fingers, peel off and discard the blackened skin.

Dice peeled poblanos, removing inner ribs and seeds.

In a heavy 5-quart pot, melt the butter over medium-high heat. Add the onion and celery and cook, stirring occasionally, until slightly softened but not browned, about five minutes.

Stir in garlic and cook one minute more.

Add broth, raw chicken tenders, and potatoes to pot and raise heat to high until liquid comes to a boil. Then reduce heat to maintain a simmer and cook until chicken is just opaque throughout. (This should only take a few minutes.) Remove chicken to a plate or cutting board, cool slightly, and shred with two forks.

Add salt, cumin, and chili powder, and continue simmering until potatoes are tender.

Add corn and beans, along with reserved diced poblanos and shredded chicken, and simmer until warmed through.

Off the heat, stir in half and half, lime juice, and cilantro.