Roast the Poblano Peppers: Preheat your oven to 400°F (200°C) or prepare a gas burner. If using the oven, place whole poblano peppers on a baking sheet. Roast for 20-25 minutes, turning occasionally, until the skins are blistered and charred. If using a gas burner, hold each pepper over the flame with tongs, rotating until the skin is blackened on all sides. Roasting the peppers softens their flesh and develops a beautiful smoky flavor, making them easier to peel and more delicious.
Steam and Peel: Immediately transfer the hot peppers to a heatproof bowl and cover tightly with plastic wrap, or place them in a paper bag and seal. Let them steam for 10-15 minutes. Steaming the peppers helps loosen their skins, making them incredibly easy to peel and preventing a tough texture in your final dish. Once cooled, carefully peel off the skins (it's okay if a few bits remain), make a slit down one side of each pepper, and gently remove the seeds and membranes. Be careful not to tear the peppers too much, as they will hold the filling.
Prepare the Filling: While the peppers are steaming, heat 1 tablespoon of olive oil in a large skillet over medium heat. Add the diced onion and cook for 5-7 minutes until softened and translucent, stirring occasionally. Sautéing the onion first creates a fragrant aromatic base, layering deep flavors into your chicken and bean filling. Add the minced garlic and cook for another minute until fragrant.
Combine Filling Ingredients: Stir in the shredded chicken, rinsed black beans, thawed corn, cumin, chili powder, smoked paprika, salt, and pepper. Cook for 3-5 minutes, stirring to combine and heat through. Remove from heat and stir in 0.75 cup of the shredded cheese. The cheese will melt slightly into the warm filling, binding it together and adding rich flavor.
Stuff and Arrange: Pour the chicken broth or salsa into the bottom of a 9x13 inch baking dish. This liquid will keep the peppers moist and add flavor as they bake. Carefully fill each poblano pepper with the chicken and black bean mixture. Arrange the stuffed peppers in the baking dish.
Bake to Perfection: Sprinkle the remaining 0.25 cup of shredded cheese over the top of the stuffed peppers. Bake for 20-25 minutes, or until the peppers are heated through and the cheese is bubbly and golden brown. The melted cheese creates an irresistible golden crust, signaling that your peppers are ready.
Serve and Garnish: Carefully remove the baking dish from the oven. Let the peppers cool for a few minutes before serving. Garnish with fresh chopped cilantro and serve with lime wedges, if desired. The fresh herbs and citrus add a bright, refreshing contrast to the rich, cheesy filling.