In a large pot heated to medium, add 1 pound 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 2 leeks, stirring occasionally, until they have softened, about 5 minutes.
Add poblanos and 2 ½ cups corn, stirring occasionally, 2-3 minutes.
Add remaining ½ cup corn and 1 cup 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 broth to mixture and cook until just simmering. Add ground beef back into the soup and cook another 2-3 minutes.
Stir in 1 cup 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.