Broil the poblanos on a foil-lined baking sheet until the skins are charred and blistered, about 5 to 7 minutes per side. Transfer the peppers to a bowl and cover tightly with plastic wrap — the steam will do the hard work of loosening the skins for you after 5 minutes.

Peel, stem, and seed the cooled peppers, then chop them into half-inch pieces.

Sauté the onion in oil in a large skillet over medium-high heat until softened and lightly browned, about 5 minutes. Stir in the garlic, cumin, and coriander and cook until fragrant.

Add the black beans, chopped poblanos, and a splash of water to the skillet. Cook, stirring occasionally, until the flavors merge and the mixture is heated through, about 3 minutes.

Remove the skillet from the heat and stir in the cilantro, lime juice, and half of the cheese. Season with salt and pepper to taste.

Whisk the tomato sauce, vegetable broth, and chipotle chiles in a medium saucepan. Bring to a simmer over medium heat and cook until slightly thickened, about 10 minutes.

Brush both sides of the tortillas lightly with oil and stack them on a plate. Cover with a damp paper towel and microwave until warm and pliable, about 1 minute.

Spread a thin layer of sauce over the bottom of a 13 by 9-inch baking dish. Place a portion of the bean mixture in the center of each tortilla, roll tightly, and arrange seam-side down in the dish.

Pour the remaining sauce over the enchiladas and sprinkle with the remaining cheese. Cover with foil and bake at 400 degrees until the sauce is bubbling, about 15 minutes.

Remove the foil and continue to bake until the cheese is lightly browned, about 5 minutes. Serve hot, garnished with extra cilantro.