One 5-ounce bunch of cilantro, leaves and stems very coarsely chopped
3/4 cup freshly grated Pecorino Romano cheese (3 ounces)
Salt and freshly ground pepper
Preheat the broiler. Rub the poblano chiles lightly with olive oil. Broil the poblanos for about 5 minutes as close to the heat source as possible, turning the chiles once, until they are charred all over. Transfer the poblanos to a medium bowl, cover them with plastic wrap and let stand for 5 minutes. Rub the skin off the chiles with a paper towel and discard the stems and seeds.
In a medium saucepan, combine the half-and-half with the husked tomatillos and the roasted chiles. Simmer over moderate heat until the tomatillos are just tender, about 10 minutes. Using a slotted spoon, transfer the tomatillos and chiles to a blender. Add the chopped cilantro and 1/2 cup of the half-and-half and puree until the mixture is smooth and creamy.
Stir the puree into the saucepan, then stir in the Pecorino Romano cheese and season with salt and pepper. Simmer the soup until the Pecorino Romano cheese is melted, about 3 minutes. Ladle the green chile soup into bowls and serve right away.