Step 1: On a medium-hot grill or hot grill pan, char the corn all over, 15–20 minutes. Transfer to a platter and set aside until cool enough to handle.
Step 2: Working over a large bowl, slice the corn kernels off each cob, scraping the cob with the knife to extract the flavorful juices. Halve 5 of the bare corn cobs crosswise, discarding the rest. Set the kernels and cobs aside.
Step 3: In a medium pot over medium heat, melt the butter. When the foam begins to subside, add the onion, celery, poblano, garlic, oregano, and bay leaf. Cover and cook, stirring occasionally, until the onion softens, 7–8 minutes. Add the reserved corn kernels and cobs, milk, potatoes, and cream. Bring to a boil, cover, and lower the heat to maintain a simmer. Cook, stirring occasionally, until the potatoes are tender, about 25 minutes. Remove and discard the cobs and bay leaf. Transfer 1½ cups of the soup to a blender and purée until smooth. Stir the puréed soup back into the pot of remaining soup to thicken. Season with salt and the ancho chile powder, then ladle into wide soup bowls and garnish with the cilantro, crema, cotija, and additional ancho chile powder. Serve with lime wedges.
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