Preheat the oven to 425°F (220°C). Line a large baking sheet with parchment paper or lightly oil it. Rinse and dry the poblano peppers, then rub them with 2 tablespoons olive oil, 1/2 teaspoon kosher salt, and 1/4 teaspoon black pepper. Arrange the peppers in a single layer and roast for 15–20 minutes, turning once halfway through, until the skins are blistered in spots and the peppers are softened but not collapsing.

Transfer the hot roasted peppers to a large bowl and cover tightly with a plate or foil. Let them steam for about 10 minutes to loosen the skins. When cool enough to handle, gently peel away the loosest skin. It’s fine if some skin remains.

While the peppers roast and steam, heat 1 tablespoon olive oil in a large skillet over medium heat. Add the chopped onion and cook for 4–5 minutes, stirring, until softened and just starting to turn golden at the edges. Add the minced garlic and cook for 30 seconds more, stirring often so it doesn’t burn.

Add the cooked rice, black beans, corn, and drained diced tomatoes with green chiles to the skillet. Stir to combine. Sprinkle in the cumin, chili powder, smoked paprika, 1/2 teaspoon kosher salt, and 1/4 teaspoon black pepper. Cook for 3–4 minutes, stirring, until heated through and the flavors meld. Taste and adjust seasoning. Turn off the heat, then stir in the chopped cilantro (if using) and 1 cup of the shredded cheese, mixing until the cheese starts to melt and the filling holds together.

Place the roasted peppers on a cutting board. Using a sharp paring knife, cut a slit down the length of each pepper, starting just below the stem and stopping before the tip to form a pocket. Gently use your fingers or a small spoon to remove the seeds and any clumps of white membrane, trying not to tear the sides.

Lightly oil or spray a 9×13-inch baking dish. Spoon the filling into each pepper, packing it in gently without forcing it so hard that the pepper splits. Use all of the filling if possible. Arrange the stuffed peppers snugly in the baking dish, slit side up. Sprinkle the remaining 1/2 cup shredded cheese evenly over the tops.

Reduce the oven temperature to 375°F (190°C). Bake the stuffed peppers for 15–20 minutes, until the cheese is melted, lightly golden in spots, and the peppers are fully tender. For extra browning, place under the broiler for 1–2 minutes, watching closely so they don’t burn.

While the peppers bake, whisk together the sour cream (or Greek yogurt), milk, lime zest, lime juice, and 1/4 teaspoon salt in a small bowl. Adjust with a splash more milk if needed to reach a drizzleable consistency, similar to a light crema. Taste and adjust lime or salt to your liking.

Let the baked poblano peppers rest for 5 minutes after removing them from the oven. Spoon or drizzle the creamy lime topping over the peppers or serve it on the side. Garnish with extra chopped cilantro, sliced green onions or red onion, and lime wedges. Serve warm, optionally with rice, salad, or tortilla chips on the side.