To roast peppers: Preheat the broiler. Cut poblanos in half lengthwise and remove stems. If you don't want a lot of heat (or none at all) remove seeds and membranes. I like to at least leave in the membranes for a little heat; it really adds to the overall flavor. Arrange the poblanos on a parchment-lined sheet pan, skin side up. Position the pan 4-6 inches under the broiler; cook until charred black, about 8-10 minutes. Transfer the poblanos to a bowl or place in paper bag, cover or seal and let steam for 10 minutes, then peel and chop the peppers, discarding the skin. Set aside.
Make the soup: In a large pot heated to medium, add the ground beef. Cook, stirring often, until the fat is rendered and the beef has begun to brown, about 8-10 minutes. Using a slotted spoon, remove and reserve the beef, leaving the fat in the pan.
Add the leeks, stirring occasionally, until they have softened, about 5 minutes.
Add the poblanos and 2 1/2 cups of the corn, stirring occasionally, 2-3 minutes.
Add remaining 1/2 cup of corn and 1 cup of the chicken or vegetable broth into a blender and blend until smooth (this step is optional but adds a nice sweetness to the broth, plus thickens it a little).
Add final 7 cups of broth to mixture and cook until just simmering. Add the ground beef back into the soup and cook another 2-3 minutes.
Stir in the cream, being careful not to let the soup boil too hard so the cream doesn't separate.
Season with the salt and pepper, to taste.
Serve immediately. Leftovers refrigerate well.