Adjust an oven rack to the upper-middle position and heat the broiler. Arrange the poblanos on a foil-lined baking sheet and broil, turning as needed, until the skins are blackened and blistered on all sides, about 10 minutes.

Transfer the charred chiles to a bowl and cover tightly with plastic wrap; let them steam until the skins loosen, about 10 minutes. Once cool enough to handle, peel the chiles, discard the stems and seeds, and chop the flesh into half-inch pieces.

Process the tomatillos, chopped onion, cilantro, broth, cream, oil, whole garlic cloves, lime juice, sugar, salt, and pepper in a food processor or blender until the sauce is completely smooth.

Heat the remaining oil in a large skillet over medium heat until it shimmers. Add the remaining chopped onion and cook until softened and translucent, about 5 minutes. Stir in the minced garlic, chili powder, coriander, and cumin and cook until the spices are fragrant.

Stir the black beans and a portion of the tomatillo sauce into the skillet. Coarsely mash the beans with a fork or potato masher to create a thick base, then stir in the chopped poblanos and half of the shredded cheese until combined.

Heat the oven to 450 degrees. Lightly brush the tortillas with oil and microwave them between damp paper towels until soft and pliable—this ensures they roll easily without tearing.

Spread a layer of tomatillo sauce over the bottom of a 13 by 9-inch baking dish. Spoon the bean filling down the center of each tortilla, roll tightly, and arrange them seam-side down in the dish.

Pour the remaining sauce over the enchiladas and sprinkle with the remaining cheese. Bake until the sauce is bubbling and the cheese is melted and beginning to brown, about 15 minutes. Serve hot.