How to Make It
Heat broiler. On a broilerproof baking sheet, broil the pepper, turning occasionally, until charred, 8 to 12 minutes. Wrap in a paper towel; let cool for 10 minutes. Use the paper towel to slide off the skin. Remove the seeds.
In a blender, puree the pepper with 2 tablespoons of the chicken broth; transfer to a bowl. Rinse out the blender.
Meanwhile, melt the butter in a large saucepan over medium heat. Add the onion and cook, stirring occasionally, until tender (do not let it brown), 8 to 10 minutes.
Add the corn, the remaining 2½ cups of chicken broth, ¾ teaspoon salt, and ¼ teaspoon pepper and bring to a boil. Reduce heat and simmer until the corn is tender, 10 to 15 minutes.
In the blender, working in batches, puree the soup until smooth, adjusting the consistency with water as necessary. (Alternatively, use a handheld immersion blender in the pot.)
Serve the soup with a drizzle of the cream and the poblano puree; sprinkle with the cilantro.