On a medium hot grill or hot grill pan, char the corn all over, 12-15 minutes. Set aside until cool enough to handle.
Turn a small dipping sauce bowl over and place in the bottom center of a large bowl. Position each ear of corn lengthwise on the small bowl and slice the corn kernels off each cob, scraping the cob with the knife to extract any juices. Repeat with all ears of corn.
Cut 3-4 bare corn cobs in half, discarding the rest. Set the corn kernels and cobs aside.
In a Dutch oven or soup pot over medium heat, melt the butter. Add the onion, celery, poblano, garlic, salt, oregano, and bay leaf. Cover and sweat the vegetables, stirring occasionally, until the onion softens, about 6 minutes.
Remove lid. Add the corn kernels and cobs, potatoes, milk, cream and ancho powder (or chile powder of choice). Bring to a boil, cover, and lower the heat to simmer. Cook, stirring occasionally, about 25 minutes. Test potatoes with fork to be they are tender yet cooked. Carefully remove and discard the cobs and bay leaf.
Transfer 2 cups of the soup to a blender and purée until smooth. Be careful and leave gap in lid to let steam out and cover with towel.
Stir the thick puréed soup back into the pot of remaining soup to thicken. Season with salt and the ancho chile powder to taste.
Divide into soup bowls and garnish with the cilantro, Mexican crema, cotija cheese crumbles and additional ancho chile powder. Serve with lime wedges.