In a large pot over medium-high heat, melt the butter. Add the onion, celery, poblano, and season with a pinch of salt and pepper. Cook, stirring occasionally, until the onion softens, about 7-8 minutes.
Add the garlic, chile powder, and oregano, and saute for about 1 minute, until fragrant.
Add the chicken stock, and potatoes. Bring to a boil, then lower the heat to maintain a simmer. Cook, stirring occasionally, until the potatoes are tender, about 15 minutes.
Stir in the corn, cream and sugar. Cook for five minutes, until warmed through.
Transfer 1½ cups of the soup to a blender and purée until smooth. Stir the puréed soup back into the pot of remaining soup.
Add cotija cheese, cilantro, and lime juice and season to taste with salt and pepper.
Serve garnished with additional cilantro, cotija, chile powder and crema. Serve with lime wedges.