On a hot grill or hot grill pan, char the corn all over, 10-12 minutes. Set aside until cool enough to handle.
On a sheet pan, cut the corn kernels off each cob. Use the back of your knife to scrape each bald cob to extract the corn milk. Reserve 1 cup of just the corn kernels and set aside for topping. Take 4 of the cobs, cub them in half, and set them aside.
Begin by heating the oil in a large, heavy-bottom pot over medium heat. Add the onions, green chilies, garlic, and cook on low heat for 3-4 minutes or until the onions become tender.
Add butter to the pot and increase heat to medium. Once melted, whisk in flour until well combined.
Stirring constantly, gradually whisk in the half and half, crema, and seasonings (salt, pepper, bay leaf, chili powder, and oregano). Add the reserved corn cobs and increase heat to high to bring everything to a boil for 1 minute. Reduce heat to medium and cook for 25 minutes. Remove and discard the cobs and bay leaf.
Transfer 1½ cups of the soup to a separate container and reserve to the side. Use an immersion blender* to puree the soup in the pot to desired consistency. Stir back in the reserved soup.
Ladle soup into bowls and garnish with reserved corn, cilantro, crema, cotija cheese, and chile powder, and hot sauce. Serve with lime wedges.