Char the corn kernels in a hot, dry skillet, undisturbed in batches, until blackened in spots, about 8-10 minutes.
Char the poblanos over a flame or under a broiler until blistered. Steam covered for 10 minutes, then peel, seed, and dice.
Melt butter, cook onion 5 minutes until softened, then add garlic for 30 seconds.
Sprinkle in flour and stir constantly for 1-2 minutes to make a roux.
Slowly whisk in the broth. Add corn cobs if using.
Add diced potatoes and simmer 15 minutes until tender. Remove and discard the cobs.
Stir in charred corn, diced poblanos, and cream. Simmer 5 minutes. Season with salt and pepper.
Ladle into bowls and top with cilantro and lime wedges.